Efficient Estimating Functions for Stochastic Differential Equations PDF Download

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 168

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Author:
Publisher:
ISBN: 9788770789608
Category :
Languages : en
Pages :

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Author: Jaya P. N. Bishwal
Publisher: Springer
ISBN: 3540744487
Category : Mathematics
Languages : en
Pages : 271

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Book Description
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.

Author: Mathieu Kessler
Publisher: CRC Press
ISBN: 1439849404
Category : Mathematics
Languages : en
Pages : 509

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Book Description
The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a spectrum of estimation methods, including nonparametric estimation as well as parametric estimation based on likelihood methods, estimating functions, and simulation techniques. Two chapters are devoted to high-frequency data. Multivariate models are also considered, including partially observed systems, asynchronous sampling, tests for simultaneous jumps, and multiscale diffusions. Statistical Methods for Stochastic Differential Equations is useful to the theoretical statistician and the probabilist who works in or intends to work in the field, as well as to the applied statistician or financial econometrician who needs the methods to analyze biological or financial time series.

Author: Dominique Jean-Marie Nocturne
Publisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 266

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A method of estimation leading to asymptotically efficient estimators for the parameters of certain stochastic processes is developed. Results are applied to estimation of parameters for Markov chains, econometric problems, and continuous time Markov processes.

Author: Carlos A. Braumann
Publisher: John Wiley & Sons
ISBN: 1119166063
Category : Mathematics
Languages : en
Pages : 299

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Book Description
A comprehensive introduction to the core issues of stochastic differential equations and their effective application Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance offers a comprehensive examination to the most important issues of stochastic differential equations and their applications. The author — a noted expert in the field — includes myriad illustrative examples in modelling dynamical phenomena subject to randomness, mainly in biology, bioeconomics and finance, that clearly demonstrate the usefulness of stochastic differential equations in these and many other areas of science and technology. The text also features real-life situations with experimental data, thus covering topics such as Monte Carlo simulation and statistical issues of estimation, model choice and prediction. The book includes the basic theory of option pricing and its effective application using real-life. The important issue of which stochastic calculus, Itô or Stratonovich, should be used in applications is dealt with and the associated controversy resolved. Written to be accessible for both mathematically advanced readers and those with a basic understanding, the text offers a wealth of exercises and examples of application. This important volume: Contains a complete introduction to the basic issues of stochastic differential equations and their effective application Includes many examples in modelling, mainly from the biology and finance fields Shows how to: Translate the physical dynamical phenomenon to mathematical models and back, apply with real data, use the models to study different scenarios and understand the effect of human interventions Conveys the intuition behind the theoretical concepts Presents exercises that are designed to enhance understanding Offers a supporting website that features solutions to exercises and R code for algorithm implementation Written for use by graduate students, from the areas of application or from mathematics and statistics, as well as academics and professionals wishing to study or to apply these models, Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance is the authoritative guide to understanding the issues of stochastic differential equations and their application.

Author: Eduardo Rossi
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Maximum likelihood estimation (MLE) of stochastic differential equations (SDEs) is difficult because in general the transition density function of these processes is not known in closed form, and has to be approximated somehow. An approximation based on efficient importance sampling (EIS) is detailed. Monte Carlo experiments, based on widely used diffusion processes, evaluate its performance against an alternative importance sampling (IS) strategy, showing that EIS is at least equivalent, if not superior, while allowing a greater flexibility needed when examining more complicated models.

Author: Simo Särkkä
Publisher: Cambridge University Press
ISBN: 1316510085
Category : Business & Economics
Languages : en
Pages : 327

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With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Author: Yanqiao Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages : 222

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There are two sources of information available in empirical research in finance: one corresponding to historical data and the other to prices currently observed in the markets. When proposing a model, it is desirable to use information from both sources. However in modern finance, where stochastic differential equations have been one of the main modeling tools, the common models are typically different for historical data and for current market data. The former are usually assumed to be time homogeneous, while the latter are typically time in-homogeneous. This practice can be explained by the fact that a time-homogeneous model is stationary and easier to estimate, while time-inhomogeneous model are required in order to replicate market data sufficiently well without creating arbitrage opportunities. In this thesis, we study methods of statistical inference, both parametric and non-parametric, for stochastic differential equations with time-dependent parameters. In the first part, we propose a new class of stochastic differential equation with time-dependent drift and diffusion terms, where some of the parameters change according to a hidden Markov process. We show that under some technical conditions this innovative way of modeling switching times renders the resulting model stationary. We also explore different approaches to estimate parameters in our proposed model. Our simulation studies demonstrate that the parameters of the model can be efficiently estimated by using a version of the filtering method proposed in the literature. We illustrate our model and the proposed estimation method by applying them to interest rate data, and we detect significant time variations in early 1980s, when targets of the monetary policy in the United States were changed. One of the known drawbacks of parametric models is the risk of model misspecification. In the second part of the thesis, we allow the drift to be time-dependent and nonparametric, and our objective is to estimate it using a single trajectory of the process. The main idea underlying this method is to approximate the time-dependent function with a sequence of polynomials. Since we can estimate efficiently only a finite number of parameters for any finite length of data, in our method we propose to relate the number of parameters to the length of the observed trajectory. This idea is similar to the method of sieves proposed by Grenander (Abstract Inference, 1981). The asymptotic analysis that we present is based on the assumption that the length of available data $T$ increases to infinity. We investigate two cases, one is a Brownian motion with time-dependent drift and the other corresponds to a class of mean-reverting stochastic differential equations with time-dependent mean-reversion level. In both cases we prove asymptotic consistency and normality of a modified maximum likelihood estimator of the projected time-dependent component. The main challenge in proving our results in the second case stems from two features of the problem: one is due to the fact that coefficients of projections change with $T$ and the other is related to the confounding effect between the mean-reversion speed and the level function. By applying our method to the same interest rate data we use in the first part, we find another evidence of time-variation in the drift term.

Author: Eckhard Platen
Publisher: Springer Science & Business Media
ISBN: 364213694X
Category : Mathematics
Languages : en
Pages : 868

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Book Description
In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.