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Conditional Quasi-Monte Carlo with Constrained Active Subspaces

Sifan Liu
Dec 2022
摘要
Conditional Monte Carlo or pre-integration is a useful tool for reducingvariance and improving regularity of integrands when applying Monte Carlo andquasi-Monte Carlo (QMC) methods. To choose the variable to pre-integrate with,one need to consider both the variable importance and the tractability of theconditional expectation. For integrals over a Gaussian distribution, one canpre-integrate over any linear combination of variables. Liu and Owen (2022)propose to choose the linear combination based on an active subspacedecomposition of the integrand. However, pre-integrating over such selecteddirection might be intractable. In this work, we address this issue by findingthe active subspaces subject to the constraints such that pre-integration canbe easily carried out. The proposed method is applied to some examples inderivative pricing under stochastic volatility models and is shown tooutperform previous methods.
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