Abstract
Conditional value at risk (CVaR) is one kind of widely used risk measurement in the practice risk management. This paper generalizes CVaR to conditional expectation and looks into its estimation and optimization. Owing to its randomness and complexities, Monte Carlo method is employed to estimate the conditional expectation. We also use Importance Sampling as variance reduction method and Optimal Computing Budget Allocation to make a more efficient use of simulation resources. The optimization problem of conditional expectation is not a deterministic problem. Therefore, we propose a new optimization framework, called Adaptive Global and Local Search for Conditional Expectation, which is a gradient-free method. This framework base on Adaptive Global and Local Search for Quantile-based Constraint problems, we implement the concept of neighborhood; use both local search and global search to find the optimal solution. The numbers of samples in both regions change by iterations. In addition, Latin Hyperball Sampling is used in the local search region to determine the sample points rather than random sampling. Last but not least, we employ Kolmogorov–Smirnov Test to determine whether the nearest point should share its observations to the optimal solution. In the end, a numerical study shows the efficiency and efficacy of our proposed method, which is worth doing further investigation.