Efficient estimation of a risk measure requiring two-stage simulation optimization

This paper is concerned with the efficient estimation of the risk measure of a system where the estimation requires solving a two-stage simulation optimization problem. The first stage samples risk factors that specify a second stage simulation optimization problem. The second stage solves a simulation optimization problem and outputs the best performance of the system under the realized risk factors, which are then aggregated across all first stage samples to produce an estimate of the risk measure. Applications of such an estimation scheme arise frequently in important industries such as financial, healthcare, logistics, and manufacturing. Because a large number of first stage samples are typically needed, each of which requires solving a computationally expensive simulation optimization problem, the two-stage simulation optimization approach faces a major computational efficiency challenge. In response to this challenge, this paper proposes a sequential simulation budget allocation procedure that determines the allocation of simulation budget based on a score known as revised probability of sign change for each decision under each scenario. The consistency of the proposed procedure is proved and the computational efficiency gain of the proposed is demonstrated using both benchmark test functions and two test cases in the context of financial portfolio risk estimation and healthcare system resilience estimation.