First Workshop of the Freiburg-Strasbourg Research Group on Financial and Actuarial Mathematics

A Workshop of a FRIAS and the Strasbourg Institute for Advanced Studies (USIAS) research group.

Invited speakers

14:00 Nicole Bäuerle (Karlsruhe)
Optimal dividend pay-out with risk sensitive preferences.

15:00 Karl-Theodor Eisele (Strasbourg)
Modelling surrender amount and profit sharing for life-insurance

Abstract: Nicole Bäuerle: Optimal dividend pay-out with risk sensitive preferences.

We consider a discrete-time dividend payout problem with risk sensitive shareholders. After briefly recalling the classical risk-neutral case we discuss two different approaches: In the first model we maximise the expected utility of discounted dividends until ruin. In the second model we consider the non-expected recursive utility of the dividends. Within such frameworks not only the expected value of the dividends is taken into account but also their variability. Our approach is motivated by a remark in Gerber and Shiu (2004). We prove that, even in these general settings, the optimal dividend policy is a band policy. Next, an explicit example is provided, in which the optimal policy is shown to be of a barrier type. Finally, we present some numerical studies and discuss the influence of the risk sensitive parameter on the optimal dividend policy. The talk is based on joint papers with Anna Jaśkiewicz.

Abstract: Karl-Theodor Eisele: Modelling surrender amount and profit sharing for life-insurance.

The central tool in the classical theory of life-insurance is the mathematical provision, defined as the actuarial value of the difference between the insurers and the policyholders engagements. However the policyholders right of withdrawal is not incorporated in it, and the participation of benefits in most cases neither. The withdrawal amount is legally based on the mathematical provision; thus the introduction of the withdrawal amount as a part of the insurers engagements leads inevitably to a circuity between these two notions. We present a comprehensive modelling of life-insurance contracts which in- tegrates withdrawal amounts and opens at the same time the the possibility of so-called cliquet-style participations in benefits. Evidently the model can no longer be linear as it is in the classical life-insurance. Also the equality between retrospective and prospective version of the mathematical provision (see Wolfsdorf: Versicherungsmathematik I.4, Satz 5) fails now. Nevertheless, a fixed-point theorem by contraction yields a unique solution to the model. With Ph. Artzner and E. Knobloch