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Numerical methods for nonlinear PDEs in finance. (English) Zbl 1229.91337

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, 503-528 (2012).
Summary: Several examples of nonlinear Hamilton Jacobi Bellman (HJB) partial differential equations are given which arise in financial applications. The concept of a visocisity solution is introduced. Sufficient conditions which ensure that a numerical scheme converges to the viscosity solution are discussed. Numerical examples based on an uncertain volatility model are presented which show that seemingly reasonable discretization methods (which do not satisfy the sufficient conditions for convergence) fail to converge to the viscosity solution.
For the entire collection see Zbl 1259.91001.

MSC:

91G60 Numerical methods (including Monte Carlo methods)
49N10 Linear-quadratic optimal control problems
49M25 Discrete approximations in optimal control

Citations:

Zbl 1259.91001
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