Numerical Solution of Stochastic Differential Equation with jumps in finance 1st edition by Eckhard Platen,Nicola Bruti Liberati 3642120571 9783642120572

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 ISBN 10:3642120571

 ISBN 13:9783642120572

Author: Eckhard Platen,Nicola Bruti Liberati

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 quantitativemethods, 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.

Numerical Solution of Stochastic Differential Equation with jumps in finance 1st Table of contents: 

Stochastic Differential Equations with Jumps

Exact Simulation of Solutions of SDEs

Benchmark Approach to Finance and Insurance

Stochastic Expansions

Introduction to Scenario Simulation

Regular Strong Taylor Approximations with Jumps

Regular Strong Itô Approximations

Jump-Adapted Strong Approximations

Estimating Discretely Observed Diffusions

Filtering

Monte Carlo Simulation of SDEs

Regular Weak Taylor Approximations

Jump-Adapted Weak Approximations

Numerical Stability

Martingale Representations and Hedge Ratios

Variance Reduction Techniques

Trees and Markov Chain Approximations

Solutions for Exercises

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