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

In: Stochastic Processes And Applications To Mathematical Finance

Author

Listed:
  • Huyên PHAM

    (Laboratoire de Probabilités et Modèles Aléatoires CNRS, UMR 7599, Université Paris 7, France)

Abstract

We 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.

Suggested Citation

  • Huyên PHAM, 2007. "Numerical Approximation by Quantization for Optimization Problems in Finance under Partial Observations," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 17, pages 275-296, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812770448_0017
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