In technical analysis of security finance securities trading, the stochastic Oscillator technical analysis oscillator is a momentum technical analysis momentum indicator that uses support and resistance levels. George Lane technical analysis Dr. George Lane promoted this indicator in the 1950s. The term stochastic refers to the location of a current price in relation to its price range over a period of time. ref Murphy, John J. 1999 . http stockcharts.com school doku.php?id chart school trading strategies john murphy s ten laws John Murphy s Ten Laws of Technical Trading . ref This method attempts to predict price turning points by comparing the closing price of a security to its price range. The indicator is defined as follows math K 100 frac text closing price text L text H text L , math where H and L are respectively the highest and the lowest price over the last math n math periods, and math D text 3 period exponential moving average of K. math In working with D it is important to remember that there is only one valid signal a divergence between D and the analyzed security. ref name Lane Lane, George M.D. May June 1984 Lane s Stochastics, second issue of Technical Analysis of Stocks ... of the recent range before turning points. The Stochastic oscillator is calculated Where ... analyst, is one of the first to publish on the use of stochastic oscillators to forecast prices ... prices will start to retreat from the upper boundaries of the range, causing the stochastic indicator ... John L year 2004 publisher Wiley location Hoboken, NJ isbn 0 471 58455 X pages 144 145 ref File Stochastic divergence.jpg thumb right 250px Stochastic divergence. An alert or set up is present when the D .... An event known as stochastic pop occurs when prices break out and keep going. This is interpreted ... links http www.investopedia.com terms s stochasticoscillator.asp Stochastic Oscillator at Investopedia technical analysis DEFAULTSORT Stochastic Oscillator Category Technical indicators ceb Osilador ... more details
Expert subject mathematics date May 2009 In mathematics, stochastic geometry is the study of random spatial patterns. At the heart of the subject lies the study of random point patterns. This leads to the theory of Point process spatial point processes , hence notions of Palm conditioning, which extend to the more abstract setting of random measure s. Models There are various models for point processes, typically based on but going beyond the classic homogeneous Poisson process Poisson point process the basic model for complete spatial randomness to find expressive models which allow effective statistical methods. The point pattern theory provides a major building block for generation of random object processes, allowing construction of elaborate random spatial patterns. The simplest version, the Boolean model probability theory Boolean model , places a random compact object at each point of a Poisson point process. More complex versions allow interactions based in various ways on the geometry ... L. last3 Koteck first3 R. year 1995 title The analysis of the Widom Rowlinson model by stochastic ... , which in some respects can be viewed as yet another theme of stochastic geometry. It is often the case ... shapes of random polygons journal Journal of Applied Mathematics and Stochastic Analysis volume .... Tessellations in stochastic geometry can of course be produced by other means, for example by using ... W. S. last3 Mecke first3 J. year 1987 title Stochastic geometry and its applications publisher ... further under the name geometric probability . The term stochastic geometry was also used by Frisch ... first1 R. last2 Weil first2 W. year 2008 title Stochastic and Integral Geometry series Probability and Its ... 78858 4 mr 2455326 ref of stochastic geometry, which allows a view of the structure of the subject ... Stochastic geometry and architecture of communication networks journal Telecommunication Systems volume ... 1995 title Stochastic Geometry Models in Image Analysis and Spatial Statistics series CWI Tract ... more details
the field itself. Brief history Stochastic Electrodynamics is a term for a collection of research ... Spavieri and George Gillies, A quantitative assessment of stochastic electrodynamics with spin ... , Inertial Mass from Stochastic Electrodynamics , in M. G. Millis et al Frontiers of Propulsion Science ... issue 4 cite conference author Boyer, T. H. title A Brief Survey of Stochastic Electrodynamics booktitle ..., L. and Cetto, A. M. title The Quantum Dice An Introduction to Stochastic Electrodynamics location ... author de la Pena, L. and Cetto, A. M. title Contribution from stochastic electrodynamics to the understanding ... of Physics? Physics footer DEFAULTSORT Stochastic Electrodynamics Category Particle physics Category ... more details
Unreferenced stub auto yes date December 2009 Stochastic neural networks are a type of artificial neural networks , which is a tool of artificial intelligence . They are built by introducing random variations into the network, either by giving the network s Artificial neuron neurons Stochastic process stochastic transfer functions, or by giving them stochastic weights. This makes them useful tools for Optimization mathematics optimization problems, since the random fluctuations help it escape from Maxima and minima local minima . Stochastic neural networks that are built by using stochastic transfer functions are often called Boltzmann machine . Example Applications in analytical trading tools, Neural Networks made up of specific trading instruments are used to Predict future price movements of one trading instrument such packaged in VantagePoint s Predicted Stochastic indicator. DEFAULTSORT Stochastic Neural Network Category Neural networks Category Stochastic algorithms Compu AI stub ... more details
Unreferenced stub auto yes date December 2009 Stochastic hill climbing is a variant of the basic hill climbing method. While basic hill climbing always chooses the steepest uphill move, stochastic hill climbing chooses at random from among the uphill moves. The probability of selection may vary with the steepness of the uphill move. See also Stochastic gradient descent DEFAULTSORT Stochastic Hill Climbing Category Optimization algorithms and methods Compu AI stub th ... more details
notability date July 2011 one source date July 2011 Infobox Book name Stochastic Resonance title orig image Image SSR book cover.tiff 200px image caption author nowrap Mark D. McDonnell , Nigel G. Stocks , br nowrap Charles E. M. Pearce , & Derek Abbott . illustrator cover artist country UK language English language English series subject Physics , biophysics , computational neuroscience , engineering genre Non fiction science text publisher Cambridge University Press pub date 2008 english pub date media type pages 448 isbn ISBN 978 0 52188 262 0 oclc preceded by followed by Stochastic Resonance From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization, is a science text, with a foreword by Sergey M. Bezrukov and Bart Kosko , which notably explores the relationships between stochastic resonance , suprathreshold stochastic resonance , stochastic Quantization signal processing quantization , and computational neuroscience . The book critically evaluates the field of stochastic resonance , considers various constraints and trade offs in the performance of stochastic Quantization signal processing quantizer s, culminating in a chapter on the application of suprathreshold stochastic resonance to the design of cochlear implant s. The book also discusses, in detail, the relationship between dither ing and stochastic resonance . Reception The book has received a favorable book review in the journal Contemporary Physics in 2009. ref K. Alan Shore, Book reviews, Contemporary Physics 50 2, pp. 482 483. ref See also Stochastic resonance Suprathreshold stochastic resonance References reflist External links http www.cup.cam.ac.uk uk catalogue catalogue.asp?isbn 9780521882620 Book s homepage at Cambridge University Press CUP http books.google.com books?id t0JreKGK7 8C Google book entry http scholar.google.com.au scholar?cites 8813026477261011624&as sdt 2005&sciodt 0,5&hl en Citations on Google Scholar Category Physics books Category Engineering books Category 2008 ... more details
In statistics , a stochastic kernel estimate is an estimate of the transition function of a usually discrete time stochastic process . Often, this is an estimate of the conditional density function obtained using kernel density estimation . The estimated conditional distribution can then be used to derive estimates of other properties of the stochastic process , such as the stationary distribution . External links http econpapers.repec.org scripts redir.pl?u http 3A 2F 2Fwww.ibmecsp.edu.br 2Fpesquisa 2Fdownload.php 3Frecid 3D3115 h repec ibm ibmecp wpe 88 Conditional Stochastic Kernel Estimation by Nonparametric Methods Laurini, M rcio P. & Valls Pereira, Pedro L. Category Stochastic processes Category Non parametric statistics Statistics stub de bergangswahrscheinlichkeit it Probabilit di transizione ... more details
Stochastic partial differential equations SPDEs are similar to ordinary stochastic differential equations . They are essentially partial differential equations that have additional random terms. They can be exceedingly difficult to solve. However, they have strong connections with quantum field theory and statistical mechanics . See also Kardar Parisi Zhang equation Zakai equation Kushner equation math stub Category Stochastic differential equations Category Partial differential equations ... more details
In probability theory and statistics , a continuous time stochastic process , or a continuous space time stochastic process is a stochastic process for which the index variable takes a continuous set of values, as contrasted with a discrete time signal discrete time process for which the index variable takes only distinct values. An alternative terminology uses continuous parameter as being more inclusive. ref Parzen, E. 1962 Stochastic Processes , Holden Day. ISBN 0 8162 6664 6 Chapter 6 ref A more restricted class of processes are the continuous stochastic process es here the term often but not always ref name D Dodge, Y. 2006 The Oxford Dictionary of Statistical Terms , OUP. ISBN 0 19 920613 9 Entry for continuous process ref implies both that the index variable is continuous and that sample paths of the process are continuous. Given the possible confusion, caution is needed. ref name D Examples An example of a continuous time stochastic process for which sample paths are not continuous is a Poisson process . An example with continuous paths is the Ornstein Uhlenbeck process . See also Continuous signal References reflist Stochastic processes Category Stochastic processes probability stub ... more details
In statistics, a doubly stochastic model is a type of model that can arise in many contexts, but in particular in modelling time series and stochastic processes . The basic idea for a doubly stochastic model is that an observed random variable is modelled in two stages. In one stage, the distribution of the observed outcome is represented in a fairly standard way using one or more parameters. At a second stage, some of these parameters often only one are treated as being themselves random variables. In a univariate context this is essentially the same as the well known concept of Compound probability distribution compounded distribution s. For the more general case of doubly stochastic models, there is the idea that many values in a time series or stochastic model are simultaneously affected by the underlying parameters, either by using a single parameter affecting many outcome variates, or by treating the underlying parameter as a time series or stochastic process in its own right. The basic idea here is essentially similar to that broadly used in latent variable model s except that here the quantities playing the role of latent variable s usually have an underlying dependence structure related to the time series or spatial context. An example of a doubly stochastic model is the following. ref Cox, D.R., Isham, V. 1980 Point processes . Chapman and Hall. ISBN 0 412 21910 7 p.10 ref The observed values in a point process might be modelled as a Poisson process in which the rate the relevant underlying parameter is treated as being the exponential of a Gaussian process . See also Cox process References reflist Further reading Tjostheim, D. 1986 Some Doubly Stochastic Time Series Models . Journal of Time Series Analysis , 7 1 ,51 72. Category Statistical models Category Latent variable models Category Stochastic processes Category Hidden stochastic models ... more details
In finance , marginal conditional stochastic dominance is a condition under which a portfolio can be improved in the eyes of all Risk aversion risk averse investors by incrementally moving funds out of one asset or one sub group of the portfolio s assets and into another. ref Shalit, H., and Yitzhaki, S. Marginal conditional stochastic dominance, Management Science journal Management Science 40, 1994, 670 684. ref ref Chow, K. V., Marginal stochastic dominance, statistical inference, and measuring portfolio performance, Journal of Financial Research 24, 2001, 289 307. ref ref Post, T., On the dual test for SSD efficiency with an application to momentum investment strategies, European Journal of Operational Research 185 3 , 2008, 1564 1573. ref Each risk averse investor is assumed to maximize the expected value of an increasing, concave von Neumann Morgenstern utility function . All such investors prefer portfolio B over portfolio A if the portfolio Return finance return of B is Stochastic dominance second order stochastically dominant over that of A roughly speaking this means that the density ... theory mean variance analysis applies. The presence of marginal conditional stochastic dominance ... stochastic dominance only considers incremental portfolio changes involving two sub groups .... ref Zhang, Duo, A demonstration of the non necessity of marginal conditional stochastic dominance ... Testing for marginal conditional stochastic dominance Yitzhaki and Mayshar ref Yitzhaki,Shlomo, and Mayshar ... inefficiency which works even when the necessary conditional of marginal conditional stochastic ... for stochastic dominance efficiency, Journal of Finance 58 5 , 2003, 1905 1932. ref ref Kuosmanen, T., Efficient diversification according to stochastic dominance criteria, Management Science 50, 2004, 1390 1406. ref ref Post, T., and Levy, H., Does risk seeking drive stock prices? A stochastic dominance ..., 925 953. ref ref Post, T., and Versijp, P., Multivariate tests for stochastic dominance efficiency ... more details
In the mathematics of probability , a stochastic process can be thought of as a random function mathematics function . In practical applications, the domain over which the function is defined is a time interval time series or a region of space random field . Familiar examples of time series include stock market and exchange rate fluctuations, signals such as speech, audio and video medical data such as a patient s EKG , Electroencephalography EEG , blood pressure or temperature and random movement such as Brownian motion or random walk s. Examples of random fields include static images, random topographies landscapes , or composition variations of an inhomogeneous material. Stochastic processes topics This list is currently incomplete. See also Category Stochastic processes Basic affine jump diffusion Talk Basic affine jump diffusion Bernoulli process Talk Bernoulli process Bernoulli process discrete time processes with two possible states. Bernoulli scheme s discrete time processes with N possible states every stationary process in N outcomes is a Bernoulli scheme, and vice versa. Birth death process Talk Birth death process Branching process Talk Branching process Branching random walk Talk Branching random walk Brownian bridge Talk Brownian bridge Brownian motion Talk Brownian ... stochastic process Talk Continuous stochastic process Cox process Talk Cox process Dirichlet process ... math S math . They can be modelled as stochastic processes where the domain is a sufficiently large ... Stationary process Stochastic calculus Talk Stochastic calculus It calculus Talk It calculus Malliavin ... Stratonovich integral Stochastic differential equation Talk Stochastic differential equation Stochastic process Talk Stochastic process Telegraph process Talk Telegraph process Time series Talk Time series Wiener process Talk Wiener process Category Mathematics related lists Stochastic processes topics Category Stochastic processes Category Statistics related lists ... more details
This page is concerned with the stochastic modelling as applied to the insurance industry. For other stochastic modelling applications, please see Monte Carlo method and Stochastic asset model s. For mathematical definition, please see Stochastic process . Stochastic model Stochastic means being or having a random variable. A stochastic model is a tool for estimating probability distributions of potential ... stochastic projections which reflect the random variation in the input s . Its application ... probable and some are less. Stochastic modelling A stochastic model would be to set up a projection ... leads to an investment return less than the guarantee. Stochastic modelling builds volatility ... life from more angles. Numerical evaluations of quantities Stochastic models help to assess the interactions ... to the discounted cash flow s. A stochastic model would be able to assess this latter quantity ... at these percentiles themselves. Stochastic models can be simulated to assess the percentiles of the aggregated ... using stochastic models. For instance, applying a non proportional reinsurance layer to the best ... layer. In a simulated stochastic model, the simulated losses can be made to pass through the layer ... to random variations , the stochastic model does not just use any arbitrary set of values. The asset ... data, and are expected to produce meaningful future projections. There are many such stochastic investment ... has written can also be modelled using stochastic methods. This is especially important in the general ... tailor made. Stochastic reserving models Estimating future claims liabilities might also involve ... of Stochastic Reserving Models published in the Australian Actuarial Journal , volume 12 issue 4 for a recent ... Stochastic Processes book http www.amazon.co.uk dp 0130465925 Options, Futures & Other Derivatives book http www.actuaries.org.uk files pdf life insurance GN47notes 20050902.pdf Guidance on stochastic ... 29.pdf J Li s article on stochastic reserving from the Australian Actuarial Journal, 2006 pdf http ... more details
In mathematics , especially in probability and combinatorics , a doubly stochastic matrix also called bistochastic , is a square matrix of nonnegative real number s, each of whose rows and columns sums to 1. Thus, a doubly stochastic matrix is both left stochastic matrix stochastic and right stochastic. ref cite book last Marshal, Olkin title Inequalities Theory of Majorization and Its Applications year 1979 isbn 0 12 473750 1 pages 8 ref Such a transition matrix is necessarily a square matrix if every row sums to one then the sum of all entries in the matrix must be equal to the number of rows, and since the same holds for columns, the number of rows and columns must be equal. The class of n × n doubly stochastic matrices is a convex polytope in R sup N sup where N n sup 2 sup , known as the Birkhoff polytope , B sub n sub . Its dimension is n &minus 1 sup 2 sup , since the row and column sums being equal to 1 imposes 2 n &minus 1 linear constraints not 2 n , because if the total of all n columns is n , the same must be true of the total of all n rows . The principal fact about doubly stochastic matrices is the Birkhoff von Neumann theorem . This states that the set B sub n sub of doubly stochastic matrices of order n is the convex hull of the set of permutation matrix permutation matrices of order n , and furthermore that the vertices extreme points of B sub n sub are precisely the permutation matrices. Sinkhorn s theorem states that any matrix with strictly positive entries can be made doubly stochastic by pre and post multiplication by diagonal matrix diagonal matrices . For n 2, all bistochastic matrices are unistochastic matrix unistochastic and orthostochastic matrix orthostochastic , but for larger n it is not the case. See also Stochastic matrix External links http planetmath.org encyclopedia BirkoffVonNeumannTheorem.html PlanetMath page on Birkhoff von Neumann theorem http planetmath.org encyclopedia ProofOfBirkoffVonNeumannTheorem.html PlanetMath page ... more details
Stochastic semantic analysis is an approach used in computer science as a semantic component of natural language understanding . Stochastic models generally use the definition of segments of words as basic semantic units for the semantic models, and in some cases involve a two layered approach. ref Language Understanding Using Two Level Stochastic Models by F. Pla, et al, 2001, Springer Lecture Notes in Computer Science ISBN 978 3 540 42557 1 ref Example applications have a wide range. In machine translation , it has been applied to the translation of spontaneous conversational speech among different languages. ref W. Minkera, M. Gavald b and A. Waibel Stochastically based semantic analysis for machine translation in Computer Speech & Language Volume 13, Issue 2, April 1999, Pages 177 194 ref In the area of spoken language understanding the fact that spoken sentences often do not follow the grammar of a language and involve self corrections, repetitions, and other irregularities, the use of stochastic semantic has been suggested as a natural fit to achieve robustness to deal with noise due to the spontaneous nature of spoken language. ref R. De Mori et al, Spoken language understanding in IEEE Signal Processing Magazine, May 2008 Volume 25 Issue 3, pages 50 58 ISSN 1053 5888 ref References Stochastically based semantic analysis by Wolfgang Minker, Alex Waibel, Joseph Mariani 1999 ISBN 0792385713 Notes Reflist Category Artificial intelligence compu AI stub ... more details
A stochastic differential equation SDE is a differential equation in which one or more of the terms is a stochastic process , resulting in a solution which is itself a stochastic process. SDE are used ... that describe the time evolution of probability distribution function s. The third form is the stochastic ... come in two varieties, corresponding to two versions of stochastic calculus. Stochastic Calculus ... dominating versions of stochastic calculus, the Ito stochastic calculus and the Stratonovich stochastic .... Numerical Solutions Numerical solution of stochastic differential equations and especially stochastic ... more explicit. It is also the notation used in publications on numerical methods for solving stochastic ... X u,u , mathrm d B u . math The equation above characterizes the behavior of the continuous time stochastic ... . A heuristic but very helpful interpretation of the stochastic differential equation is that in a small time interval of length the stochastic process X sub t sub changes its value by an amount .... The stochastic process X sub t sub is called a diffusion process , and is usually a Markov ... general stochastic differential equations where the coefficients and depend not only on the present ... only on present and past values of X , the defining equation is called a stochastic delay differential ... 2 big infty. math Then the stochastic differential equation initial value problem math mathrm d X t mu .... math See also Langevin dynamics Local volatility Stochastic Volatility Stochastic volatility Sethi advertising model Stochastic partial differential equations Diffusion process References cite book last Adomian first George title Stochastic systems series Mathematics in Science and Engineering 169 ... title Nonlinear stochastic operator equations publisher Academic Press Inc. location Orlando, FL year 1986 cite book last Adomian first George title Nonlinear stochastic systems theory and applications ... Dordrecht year 1989 cite book last ksendal first Bernt K. authorlink Bernt ksendal title Stochastic ... more details
Unreferenced date November 2009 In mathematics , the law of a stochastic process is the Measure mathematics measure that the process induces on the collection of Function mathematics functions from the index set into the state space. The law encodes a lot of information about the process in the case of a random walk , for example, the law is the probability measure probability distribution of the possible trajectories of the walk. Definition Let , F , P be a probability space , T some index set, and S , a measurable space . Let X T × S be a stochastic process so the map math X t Omega to S omega mapsto X t, omega math is a F , measurable function for each t T . Let S sup T sup denote the collection of all functions from T into S . The process X by way of currying induces a function sub X sub S sup T sup , where math left Phi X omega right t X t omega . math The law of the process X is then defined to be the pushforward measure math mathcal L X left Phi X right mathbf P mathbf P circ Phi X 1 math on S sup T sup . Example The law of standard Brownian motion is classical Wiener measure . Indeed, many authors define Brownian motion to be a sample continuous process starting at the origin whose law is Wiener measure, and then proceed to derive the independence of increments and other properties from this definition other authors prefer to work in the opposite direction. See also Finite dimensional distribution stochastic process DEFAULTSORT Law Stochastic Processes Category Stochastic processes probability stub ... more details
Stochastic resonance is a phenomenon that occurs in a threshold measurement system e.g. a man made instrument ... detection theory d , etc. is maximized in the presence of a non zero level of stochastic input noise ... WG title Stochastic resonance and sensory information processing a tutorial and review of application .... The three criteria that must be met for stochastic resonance to occur are Nonlinear device or system ... there must be random, uncorrelated variation added to signal of interest Stochastic resonance occurs ... systems, the addition of noise can actually improve the probability of detecting the signal this is stochastic resonance. The systems in which stochastic resonance occur are always nonlinear systems ... volume 14 pages L453 title The mechanism of stochastic resonance issue 11 ref Stochastic Resonance ... of stochastic resonance, consider the following demonstration after Simonotto et al. ref name Simonotto ... title Visual Perception of Stochastic Resonance year 1997 last1 Simonotto first1 Enrico last2 Riani ... from stochastic resonance can be improved further by blurring, or subjecting the image to low ... a new effective threshold for the measurement device. History of Stochastic Resonance Stochastic ... research cfsa people hnat finalyearproj0910 benzi on climate stochres.pdf title A Theory of Stochastic ... compared to the dramatic temperature change, however, and stochastic resonance was developed to show that the temperature change due to the weak eccentricity oscillation and added stochastic variation ... to move in a nonlinear fashion between two stable dynamic states. Stochastic Resonance in Animal Physiology Cuticular Mechanoreceptors in the Crayfish Evidence for stochastic resonance in a sensory ... E, Moss F title Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic ... higher level of analysis establish behavioral effects of stochastic resonance in other organisms ... by stochastic resonance journal Nature volume 380 issue 6570 pages 165 8 year 1996 month March pmid ... more details
Stochastic diffusion search SDS was first described in 1989 as a population based, pattern matching algorithm Bishop, 1989 . It belongs to a family of swarm intelligence and naturally inspired search and optimisation algorithms which includes ant colony optimization , particle swarm optimization and genetic algorithm s. Unlike stigmergetic communication employed in ant colony optimization , which is based on modification of the physical properties of a simulated environment, SDS uses a form of direct one to one communication between the agents similar to the tandem calling mechanism employed by one species of ants, Leptothorax acervorum . In SDS agents perform cheap, partial evaluations of a hypothesis a candidate solution to the search problem . They then share information about hypotheses diffusion of information through direct one to one communication. As a result of the diffusion mechanism, high quality solutions can be identified from clusters of agents with the same hypothesis. The operation of SDS is most easily understood by means of a simple analogy &ndash The Restaurant Game. The restaurant game A group of delegates attends a long conference in an unfamiliar town. Every night ... delegates decide to employ a stochastic diffusion search. Each delegate acts as an agent maintaining ... allocation Nasuto, 1999 under a variety of search conditions. References Bishop, J.M., 1989 . Stochastic ..., J.M. & Torr, P., 1992 . The Stochastic Search Network. In R. Linggard, D.J. Myers, C. Nightingale .... Myatt, D.R., Bishop J.M. and Nasuto, S.J., 2004 . Minimum Stable Convergence Criteria for Stochastic ... Allocation of Stochastic Diffusion Search. PhD Thesis. University of Reading, UK. Nasuto, S.J. & Bishop, J.M., 1999 . Convergence Analysis of Stochastic Diffusion Search. Journal of Parallel ... of Stochastic Diffusion Search. Neural Computation 98, Vienna, Austria. Whitaker, R.M., Hurley ... on Applied Computing Madrid . 574&ndash 577. Category Artificial intelligence Category Stochastic algorithms ... more details
multiple issues unreferenced December 2011 prose January 2012 A stochastic investment model tries to forecast how rate of return returns and price s on different assets or asset classes, e. g. equities or bonds vary over time. Stochastic models are not applied for making point estimation rather interval estimation and they use different stochastic process es. clarify rason different to what date January 2012 Investment models can be classified into single asset and multi asset models. They are often used for actuary actuarial work and financial plan ning to allow optimization in asset allocation or asset liability management asset liability management ALM . Single asset models Interest rate models Interest rate models can be used to price fixed income products. They are usually divided into one factor models and multi factor assets. One factor models Black Derman Toy model Black Karasinski model Cox Ingersoll Ross model Ho Lee model Hull White model Kalotay Williams Fabozzi model Merton Model Merton model Rendleman Bartter model Vasicek model Multi factor models Chen model Longstaff Schwartz model Term structure models LIBOR market model LIBOR market model Brace Gatarek Musiela model Stock price models Binomial model Black Scholes model geometric Brownian motion Inflation models Multi asset models ALM.IT GenRe model Cairns model FIM Group model Global CAP Link model Ibbotson and Sinquefield model Morgan Stanley model Russel Yasuda Kasai model Smith s jump diffusion model TSM B & W Deloitte model Watson Wyatt model Whitten & Thomas model Wilkie investment model Yakoubov, Teeger & Duval model Category Finance theories Category Mathematical finance Category Stochastic models ... more details
distinguish Continuous time stochastic process In the probability theory , a continuous stochastic process is a type of stochastic process that may be said to be continuous function continuous as a function of its time or index parameter. Continuity is a nice property for the sample paths of a process to have, since it implies that they are well behaved in some sense, and, therefore, much easier to analyse. It is implicit here that the index of the stochastic process is a continuous variable. Note that some authors ref name D Dodge, Y. 2006 The Oxford Dictionary of Statistical Terms , OUP. ISBN 0 19 920613 9 Entry for continuous process ref define a continuous stochastic process as only requiring that the index variable be continuous, without continuity of sample paths in some terminology, this would be a continuous time stochastic process , in parallel to a discrete time process . Given the possible confusion, caution is needed. ref name D Definitions Let , , P be a probability space , let T be some interval mathematics interval of time, and let X T × S be a stochastic process. For simplicity, the rest of this article will take the state space S to be the real line R , but the definitions go through mutatis mutandis if S is R sup n sup , a normed space normed vector space , or even a general metric space . Continuity with probability one Given a time t T , X is said to be continuous with probability one at t if math mathbf P left left omega in Omega left lim s to t big X s omega X t omega big 0 right. right right ... The relationships between the various types of continuity of stochastic processes are akin to the relationships ... Kloeden, Peter E. coauthors Platen, Eckhard title Numerical solution of stochastic differential equations ... title Stochastic Differential Equations An Introduction with Applications edition Sixth edition publisher Springer location Berlin year 2003 id ISBN 3 540 04758 1 See Lemma 8.1.4 Category Stochastic ... more details
math . The stochastic prediction procedure math A beta X math shall yield predictions with optimal ... a function math A X beta math which meets the above formulated two requirements. Stochastic ... of uncertainty are explicitly contained in the corresponding Bernoulli Space. The derivation of a stochastic prediction procedure is therefore based on a Bernoulli Space which represents a stochastic ... of a stochastic prediction procedures shall be illustrated by a comparison with a prediction made and published ... accuracy . In case of a stochastic prediction procedure it refers to the size of the predicted event ... Category Stochastic processes ... more details
Context date June 2009 In physics , the stochastic vacuum model is a nonperturbative, phenomenological approach to derive cross section physics cross section in quantum chromodynamics . It is deemed impossible to calculate the vacuum averages of gauge invariant quantities in QCD in a closed form, e.g. using the path integrals. But standard perturbation theory techniques don t work at distances, where the running coupling constant reaches 1. The stochastic vacuum model is based on the approximation of nonperturbative QCD as a Gaussian process. It allows to calculate Wilson loop s. References No footnotes date June 2009 reflist Field correlators in QCD A. Di Giacomo, H.G. Dosch, V.I. Shevchenko, Yu.A. Simonov, Phys. Repts. 372 319 368 2002 Pomeron Physics and QCD S. Donnachie, H.G. Dosch, P. Landshoff, O. Nachtmann C U P 2002 Category Quantum chromodynamics quantum stub ... more details
Stochastic frontier analysis SFA is a method of Model economics economic modeling . It has its starting point in the stochastic production frontier models simultaneously introduced by Aigner, Lovell and Schmidt 1977 and Meeusen and Van den Broeck 1977 . The production frontier model without random component can be written as math y i f x i beta cdot TE i math where y sub i sub is the observed scalar output of the producer i , i 1,..I, x sub i sub is a vector of N inputs used by the producer i , f x sub i sub , is the production frontier, and math beta math is a vector of technology parameters to be estimated. TE sub i sub denotes the technical efficiency defined as the ratio of observed output to maximum feasible output. TE sub i sub 1 shows that the i th firm obtains the maximum feasible output, while TE sub i sub 1 provides a measure of the shortfall of the observed output from maximum feasible output. A stochastic component that describes random shocks affecting the production process is added. These shocks are not directly attributable to the producer or the underlying technology. These shocks may come from weather changes, economic adversities or plain luck. We denote these effects with math exp left v i right math . Each producer is facing a different shock, but we assume the shocks are random and they are described by a common distribution. The stochastic production frontier will become math y i f x i beta cdot TE i cdot exp left v i right math We assume that TE sub i sub is also a stochastic variable, with a specific distribution function, common to all producers. We can also write it as an exponential math TE i exp left u i right math , where u sub i sub 0 , since we required TE sub i sub 1 . Thus, we obtain the following equation math y i f x i beta cdot exp ... of stochastic frontier production functions. Journal of Econometrics, 6 21 37. Coelli, T.J. ..., 2nd Edition. Springer, ISBN 978 0 387 24266 8. Kumbhakar, S.C. Lovell, C.A.K. 2000 Stochastic Frontier ... more details
In mathematics &mdash specifically, in stochastic processes stochastic analysis &mdash the infinitesimal generator of a stochastic process is a partial differential operator that encodes a great deal of information about the process. The generator is used in evolution equations such as the Kolmogorov backward equation which describes the evolution of statistics of the process its Lp space L sup 2 sup Hermitian adjoint is used in evolution equations such as the Fokker Planck equation which describes the evolution of the probability density function s of the process . Definition Let X 0, × R sup n sup defined on a probability space , , P be an It diffusion satisfying a stochastic differential equation of the form math mathrm d X t b X t , mathrm d t sigma X t , mathrm d B t , math where B is an m dimensional Brownian motion and b R sup n sup R sup n sup and R sup n sup R sup n × m sup are the drift and diffusion fields respectively. For a point x R sup n sup , let P sup x sup denote the law of X given initial datum X sub 0 sub x , and let E sup x sup denote expectation with respect to P sup x sup . The infinitesimal generator of X is the operator A , which is defined to act on suitable functions f R sup n sup R by math A f x lim t downarrow 0 frac mathbf E x f X t f x t . math The set of all functions f for which this limit ... , which satisfies the stochastic differential equation d X sub t sub d B sub t sub , has ... satisfies the stochastic differential equation d X sub t sub X sub t sub d ... A geometric Brownian motion on R , which satisfies the stochastic differential equation d X sub t sub ... ksendal first Bernt K. authorlink Bernt ksendal title Stochastic Differential Equations An Introduction ... 04758 1 See Section 7.3 Category Stochastic differential equations de Generator Markow Prozesse fr G n rateur ... more details
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