Optimal importance sampling with explicit formulas in continuous time
type: Item
instance of: scholarly article
title: Optimal importance sampling with explicit formulas in continuous time
zbMATH Open document ID: 1150.91019
author: Paolo Guasoni
author: Scott Robertson
published in: Finance and Stochastics
publication date: 2008-06-18T00:00:00Z
review text: In the Black-Scholes model the problem arises how to select a change of drift which minimizes the variance of Monte Carlo estimators for prices of path-dependent options. The authors follow the approach to a continuous-time setting, where the optimal deterministic drift in the Black-Scholes model is identified as the solution of a one-dimensional variational problem. The main idea is briefly summarized with an heuristic argument, which involves derivatives of non-differential Brownian paths, applies Laplace asymptotic in infinite dimensions, and assumes the validity of a minimax result. In spite of these issues, this characterization of the optimal drift is essentially correct. In continuous time the variational problem reduces to the familiar Euler-Lagrange ordinary differential equation. In the case of Asian options the optimal change of drift admits closed-form solutions.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 91G60
zbMATH DE Number: 5290175
zbMATH Keywords: Monte Carlo method
zbMATH Keywords: variance reduction
zbMATH Keywords: importance sampling
MaRDI profile type: Publication
full work available at URL: s00780-007-0053-5
OpenAlex ID: W2017986621
cites work: Q4391441
cites work: The integral of geometric Brownian motion
cites work: Q4388221
cites work: Importance Sampling, Large Deviations, and Differential Games
cites work: Dynamic importance sampling for uniformly recurrent Markov chains
cites work: BESSEL PROCESSES, ASIAN OPTIONS, AND PERPETUITIES
cites work: Counterexamples in importance sampling for large deviations probabilities
cites work: Asymptotically optimal importance sampling and stratification for pricing path-dependent options
cites work: Some Asymptotic Formulas for Wiener Integrals
cites work: Importance sampling in the Monte Carlo study of sequential tests
cites work: Q4284032
cites work: Asymptotic probabilities and differential equations
DOI: 10.1007/S00780-007-0053-5
description: scientific article; zbMATH DE number 5290175