June 2016 Optimal importance sampling for the Laplace transform of exponential Brownian functionals
Je Guk Kim
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J. Appl. Probab. 53(2): 531-542 (June 2016).

Abstract

We present an asymptotically optimal importance sampling for Monte Carlo simulation of the Laplace transform of exponential Brownian functionals which plays a prominent role in many disciplines. To this end we utilize the theory of large deviations to reduce finding an asymptotically optimal importance sampling measure to solving a calculus of variations problem. Closed-form solutions are obtained. In addition we also present a path to the test of regularity of optimal drift which is an issue in implementing the proposed method. The performance analysis of the method is provided through the Dothan bond pricing model.

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Je Guk Kim. "Optimal importance sampling for the Laplace transform of exponential Brownian functionals." J. Appl. Probab. 53 (2) 531 - 542, June 2016.

Information

Published: June 2016
First available in Project Euclid: 17 June 2016

zbMATH: 06614127
MathSciNet: MR3514296

Subjects:
Primary: 91G60
Secondary: 60F10 , 91G80

Keywords: Calculus of variation , Dothan model , Exponential Brownian functional , importance sampling , large deviations , Monte Carlo method

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 2 • June 2016
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