Numerical Approximation by Quantization for Optimization Problems in Finance under Partial Observations

Huyên Pham
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Huyên Pham: Laboratoire de Probabilités et Modèles Aléatoires CNRS, UMR 7599, Université Paris 7, France

Chapter 17 in Stochastic Processes and Applications to Mathematical Finance, 2007, pp 275-296 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe present some recent developments on optimal quantization methods for numerically feasible solutions to discrete-time optimization problems under partial information. The main problem in effective implementation is in growing dimension of the the approximating filters. We overcome this difficulty by performing a quantization of the pair process filter-observation. Dynamic programming is then applied to solve the approximated optimization problem. Several numerical applications in finance are presented for the pricing of American option or for hedging problems in the context of partially observed stochastic volatility models.

Keywords: Stochastic Calculus; Mathematical Finance; Insider Trading; Stochastic Control; Real Options; Filtering Model of Credit Risks; Stochastic Growth Models (search for similar items in EconPapers)
Date: 2007
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