Gradient Extrapolated Stochastic Kriging

• Activity Number: 79
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Risk Analysis
• Author(s): Michael Fu*+ and Huashuai Qu
• Companies: and University of Maryland
• Keywords: kriging ; response surface methodology ; simulation ; stochastic gradients ; stochastic optimization ; Monte Carlo

Abstract

For the setting of stochastic (or Monte Carlo) simulation, widely used in financial risk analysis, one design of experiments approach for optimization is response surface methodology, of which a recently introduced technique is stochastic kriging. We introduce a novel approach to enhance stochastic kriging with the availability of additional gradient information that is provided by techniques such as perturbation analysis or the likelihood ratio method. We propose Gradient Extrapolated Stochastic Kriging (GESK), which incorporates direct gradient estimates into stochastic kriging by adding extrapolated points. Since extrapolation step sizes are crucial to the performances of GESK models, we propose two different approaches to determine the step sizes. For some special settings, we show that incorporating gradient estimates leads to predictions with smaller mean squared errors (MSE); then we address the issue of approximation errors caused by extrapolation. Numerical experiments are conducted to illustrate the performance of the GESK models and compare them with existing models.