Dr. Olaf Menkens, Dublin City University (DCU), Ireland

Title: Optimising Proportional Reinsurance Using a Worst Case Scenario Approach

Abstract: This presentation considers the problem of an insurance company to optimise its reserve process by proportional reinsurance. Usually, the reinsurance level will be determined by a ruin probability constraint or by minimising the ruin probability (see e.g. Hipp and Vogt (2003), Schmidli (2001, 2002, and 2004), or Eisenberg and Schmidli (2008)). Instead of conditioning on the ruin probability, this presentation will maximise the controlled reserve process by a worst--case scenario approach.

The worst--case scenario approach has been introduced in the context of portfolio optimisation by Korn and Wilmott (2002). This approach has been extended so far in various ways (e.g. considering different utility function (Korn and Menkens (2005)), optimising investment portfolio of an insurance company (Korn (2005)), in a stochastic differential game context (Korn and Steffensen (2007)).

We start by making the so--called small claims assumption, that is the claims will be modelled as a Brownian motion with drift. Second, the claims will be modelled as the sum of a Brownian motion with drift and a Poisson process and third, claims will be modelled as a Poisson process. Results will be computed, analysed, and compared with the results of minimising the ruin probability.

This is work in progress and joint research with Ralf Korn (TU Kaiserslautern) and Mogens Steffensen (U of Copenhagen).