Journal of Applied Probability

Optimal importance sampling for the Laplace transform of exponential Brownian functionals

Je Guk Kim

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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.

Article information

J. Appl. Probab., Volume 53, Number 2 (2016), 531-542.

First available in Project Euclid: 17 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 91G60: Numerical methods (including Monte Carlo methods)
Secondary: 60F10: Large deviations 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)

Exponential Brownian functional Monte Carlo method importance sampling calculus of variation large deviations Dothan model


Kim, Je Guk. Optimal importance sampling for the Laplace transform of exponential Brownian functionals. J. Appl. Probab. 53 (2016), no. 2, 531--542.

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