A framework for adaptive Monte-Carlo procedures

Details A framework for adaptive Monte-Carlo procedures A framework for adaptive Monte-Carlo procedures

2010-01-20

arxiv.org/abs/1001.3551v2

Monte Carlo Methods and Applications 17, 1 (2011) 77-98

Economy

Quantitative Finance

Computational Finance

Scientific paper

10.1515/MCMA.2011.002

Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad and Dufresne, Fu and Su, and Arouna. We establish the convergence and asymptotic normality of the adaptive Monte Carlo estimator under local assumptions which are easily verifiable in practice. We present one way of approximating the optimal importance sampling parameter using a randomly truncated stochastic algorithm. Finally, we apply this technique to some examples of valuation of financial derivatives.

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