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Activity Number: 79
Type: Contributed
Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
Sponsor: Section on Risk Analysis
Abstract - #309279
Title: Gradient Extrapolated Stochastic Kriging
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.


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