Normalized Exponential Tilting

Abstract

This article discusses methods of risk-neutralizing multivariate probability distributions by applying exponential tilting to the joint probability density function with respect to a set of reference risks. To ensure consistent interpretations of the exponential tilting parameters, a normalization procedure is performed on the reference risks via percentile mapping to standard normal variables. The article establishes links between normalized exponential tilting and multivariate probability distortions. It provides efficient methods for computing risk-neutralized multivariate probability distributions, and it gives illustrative examples in pricing contingent claims on multiple risks.

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