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Numerical solution of stochastic differential equations in finance. (English) Zbl 1229.91347
Duan, Jin-Chuan (ed.) et al., Handbook of computational finance. Berlin: Springer (ISBN 978-3-642-17253-3/hbk; 978-3-642-17254-0/ebook). Springer Handbooks of Computational Statistics, 529-550 (2012).
Summary: This chapter is an introduction and survey of numerical solution methods for stochastic differential equations. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial systems. We include a review of fundamental concepts, a description of elementary numerical methods and the concepts of convergence and order for stochastic differential equation solvers. In the remainder of the chapter we describe applications of SDE solvers to Monte-Carlo sampling for financial pricing of derivatives. Monte-Carlo simulation can be computationally inefficient in its basic form, and so we explore some common methods for fostering efficiency by variance reduction and the use of quasi-random numbers. In addition, we briefly discuss the extension of SDE solvers to coupled systems driven by correlated noise, which is applicable to multiple asset markets.
For the entire collection see Zbl 1259.91001.

MSC:
91G60 Numerical methods (including Monte Carlo methods)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65C30 Numerical solutions to stochastic differential and integral equations
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