Approximation of jump diffusions in finance and economics

被引：18

作者：

Bruti-Liberati N. ^{[1
]}

Platen E. ^{[1
]}

机构：

[1] School of Finance and Economics, University of Technology Sydney, Broadway, NSW 2007

来源：

Computational Economics | 2007年 / 29卷 / 3-4期

基金：

澳大利亚研究理事会;

关键词：

Benchmark approach; Discrete time approximation; Growth Optimal portfolio; Jump-diffusion processes; Simulation; Strong convergence; Weak convergence;

D O I：

10.1007/s10614-006-9066-y

中图分类号：

学科分类号：

摘要：

In finance and economics the key dynamics are often specified via stochastic differential equations (SDEs) of jump-diffusion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, discrete time approximations are required. In this paper we give a survey of strong and weak numerical schemes for SDEs with jumps. Strong schemes provide pathwise approximations and therefore can be employed in scenario analysis, filtering or hedge simulation. Weak schemes are appropriate for problems such as derivative pricing or the evaluation of risk measures and expected utilities. Here only an approximation of the probability distribution of the jump-diffusion process is needed. As a framework for applications of these methods in finance and economics we use the benchmark approach. Strong approximation methods are illustrated by scenario simulations. Numerical results on the pricing of options on an index are presented using weak approximation methods. © Springer Science+Business Media, LLC 2007.

引用

页码：283 / 312

页数：29

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