Actuarial Risk Measures for Financial Derivative Pricing

Abstract

We present an axiomatic characterization of price measures that are superadditive and comonotonic additive for normally distributed random variables. The price representation derived involves a probability measure transform that is closely related to the Esscher transform, and we call it the Esscher-Girsanov transform. In a financial market in which the primary asset price is represented by a stochastic differential equation with respect to Brownian motion, the price mechanism based on the Esscher-Girsanov transform can generate approximate-arbitrage-free financial derivative prices.

Keywords: Derivative pricing, Stochastic ordering, Esscher transform, Girsanov's Theorem, Comonotonicity, Equivalent martingale measure, Feynman-Kac integration

JEL Classification: D81, G12, G13