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Huyn Pham, Wolfgang Runggaldier, Afef Sellami

Approximation by quantization of the filter process and applications to optimal stopping problems under partial observation

Keywords: Nonlinear filtering, Markov chain, quantization, stochastic gradient descent, Monte Carlo simulations, partial observation, optimal stopping

We present an approximation method for discrete time nonlinear filtering in view of solving dynamic optimization problems under partial information. The method is based on quantization of the Markov pair process filter-observation (Π, Y) and is such that, at each time step k and for a given size N_k of the quantization grid in period k, this grid is chosen to minimize a suitable quantization error. The algorithm is based on a stochastic gradient descent combined with Monte Carlo simulations of (Π, Y). Convergence results are given and applications to optimal stopping under partial observation are discussed. Numerical results are presented for a particular stopping problem: American option pricing with unobservable volatility.

Monte Carlo Methods and Applications, Walter de Gruyter

Print ISSN: 0929-9629
Volume: 11, 03/2005
Pages: 57 - 81

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