Restricted Coherent Risk Measures and Actuarial Solvency

Restricted Coherent Risk Measures and Actuarial Solvency

Actuarial Risk Measures for Financial Derivative Pricing

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 ...

Solvency capital, risk measures and comonotonicity: a review

In this paper we examine and summarize properties of several well-known risk measures that can be used in the framework of setting solvency capital requirements for a risky business. Special attention is given to the class of (concave) distortion risk measures. We investigate the relationship between these risk measures and theories of choice under risk. Furthermore we consider the problem of h...

Compositions of Conditional Risk Measures and Solvency Capital

Abstract: In this paper, we consider compositions of conditional risk measures in order to obtain time-consistent dynamic risk measures and determine the solvency capital of a life insurer selling pension liabilities or a pension fund with a single cash-flow at maturity. We first recall the notion of conditional, dynamic and time-consistent risk measures. We link the latter with its iterated pr...

Draft: Coherent Risk Measures

Part of the course was devoted to an analysis of Value at Risk and its relation to quantiles. A detailed discussion of this can be found in two papers by Artzner, Delbaen, Eber and Heath, ADEH1 and ADEH2. It will not be repeated here. We will rather concentrate on the mathematics behind the concept of coherent risk measures. They were introduced in the two mentioned papers and the mathematical ...