Computing Sensitivities for Distortion Risk Measures

Author:

Glynn Peter W.1,Peng Yijie2ORCID,Fu Michael C.3,Hu Jian-Qiang4ORCID

Affiliation:

1. Department of Management Science and Engineering, Stanford University, Stanford, California 94305;

2. Department of Management Science and Information Systems, Guanghua School of Management, Peking University, Beijing 100871, China;

3. The Robert H. Smith School of Business, Institute for Systems Research, University of Maryland, College Park, Maryland 20742;

4. Department of Management Science, School of Management, Fudan University, Shanghai 200433, China

Abstract

Distortion risk measure, defined by an integral of a distorted tail probability, has been widely used in behavioral economics and risk management as an alternative to expected utility. The sensitivity of the distortion risk measure is a functional of certain distribution sensitivities. We propose a new sensitivity estimator for the distortion risk measure that uses generalized likelihood ratio estimators for distribution sensitivities as input and establish a central limit theorem for the new estimator. The proposed estimator can handle discontinuous sample paths and distortion functions.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

Subject

General Engineering

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