Abstract

The drawdown is the loss of the surplus process compared to its historical maximum. In order to stabilize the surplus one tries to keep the surplus close the its maximum; that is, keeping the drawdown small. We use proportional reinsurance to control the drawdown and measure the time the drawdown spends below a predefined barrier. If the time in drawdown is the only criterion, the maximum will never increase under the optimal strategy, see Brinker and Schmidli (2022). To avoid this, we maximise simultaneously the increase of the maximum. Dependent on how we weight the two contradicting criteria, we obtain different strategies, of which some are surprising. Another variant of the problem is if the drawdown is only observed at the times of a renewal process. The latter case leads also to economically more reasonable decisions. (The talk is based on joint work with Leonie Brinker and Kira Dudziak.)

Speaker

Hanspeter Schmidli (University of Cologne)