A Change-of-Variable Approach to Conditional Monte Carlo
DescriptionSensitivity estimation is about estimating the derivatives of an expectation with respect to some parameters. It is one of the most important problems in simulation, which finds applications in a wide range of areas in operations research such as gradient-based simulation optimization and hedging parameter estimation of financial securities. Among various Monte Carlo methods for sensitivity estimation, the pathwise method is usually preferred due to its small variance. However, the pathwise method is not applicable when the integrand is discontinuous.Conditional Monte Carlo (CMC) is a useful simulation technique in handling the discontinuity of the integrands. Conditioning on an appropriate random vector, CMC removes the discontinuity by taking a conditional expectation, and thus enables the use of the pathwise method. However, effective use of CMC relies on an appropriate selection of the conditioning random vector. In many practical applications, this selection is problem dependent, and could be difficult in some practical cases.In this project, we propose to view CMC from a new perspective. Instead of selecting a conditioning random vector, we construct a one-to-one mapping and then employ the change-of-variable technique. By doing so, we expect to obtain new insights for CMC. The change-of-variable approach may lead to new estimators of sensitivity for cases where it is not clear how to apply traditional CMC. This project aims to investigate in detail the connection between the proposed change-of-variable approach and the traditional CMC. It is expected that the output of this project may help academic researchers better understand the traditional CMC technique, and provide practitioners with viable new estimators in various application domains.
|Effective start/end date||1/01/14 → 28/12/17|