Journal of Applied Probability

Optimal importance sampling for the Laplace transform of exponential Brownian functionals

Je Guk Kim

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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.

Article information

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

Dates
First available in Project Euclid: 17 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1466172872

Mathematical Reviews number (MathSciNet)
MR3514296

Zentralblatt MATH identifier
06614127

Subjects
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)

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

Citation

Kim, Je Guk. Optimal importance sampling for the Laplace transform of exponential Brownian functionals. J. Appl. Probab. 53 (2016), no. 2, 531--542. https://projecteuclid.org/euclid.jap/1466172872


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