Research in Actuarial Science

Compositions of Conditional Risk Measures and Solvency Capital


Reacfin’s consultant, Dr. Adrien Lebègue, together with our chairman, Pr. Pierre de Volder, have just published a scientific article that proposes routes considering time-consistent risk measures to determine the necessary capital of pension funds or insurance companies.

In this paper, the authors 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. Pr. Devolder and Dr. Lebègue first recall the notion of conditional, dynamic and time-consistent risk measures. They link the latter with its iterated property, which gives a way to construct time-consistent dynamic risk measures from a backward iteration scheme with the composition of conditional risk measures. They then consider particular cases with the conditional version of the value at risk, tail value at risk and conditional expectation measures. Finally, the authors give an application of these measures with the determination of the solvency capital of a pension liability, which offers a fixed guaranteed rate without any intermediate cash-flow.

This paper entitled “Compositions of Conditional Risk Measures and Solvency Capital” is currently available on the site of the Multidisciplinary Digital Publishing Institute