On Asymptotical Efficiency of Importance Sampling with p-order Relative Moment Minimization

The optimal parameters of candidate measures established by importance sampling are usually obtained by minimizing the quadratic criterion. To begin with, in this paper a scheme is developed for finding the alternative measure that is optimal in the sense that the p-order relative moment is minimize...

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Bibliographic Details
Main Authors: Gao, Quan-sheng, Chen, Xin
Format: Conference Proceeding
Language:English
Subjects:
Information management
Information technology
Mathematics
Monte Carlo methods
Physics
Pricing
Proposals
Sampling methods
Seminars
Sufficient conditions
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Summary:The optimal parameters of candidate measures established by importance sampling are usually obtained by minimizing the quadratic criterion. To begin with, in this paper a scheme is developed for finding the alternative measure that is optimal in the sense that the p-order relative moment is minimized. Secondly, a necessary and sufficient condition for asymptotic efficiency of the optimal change of drift is demonstrated. Lastly, the change of drift is selected through Robbins-Monro type algorithm. When pricing options via Monte Carlo simulations, several numerical examples contrasting different p values that illustrate the efficiency of the proposed method are also included, as well as an interpretation of their different performances in terms of strike prices.
DOI:10.1109/FITME.2008.67