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arXiv · 2504.03319

Stochastic Control of Drawdowns via Reinsurance under Random Inspection

Kira Dudziak·Hanspeter Schmidli
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Abstract

We consider a diffusion risk model where proportional reinsurance can be bought. In order to stabilise the surplus process, one tries to keep the drawdown, that is the difference of the surplus to its historical maximum, in an interval $[0,d)$. The observation times of the drawdowns form a renewal process. The retention levels can only be changed at the observation times either. We show that an optimal strategy exists and how it is determined. We illustrate the findings in the case of Poissonian observation times and deterministic inter-observation times.

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Kira Dudziak, Hanspeter Schmidli. 2025-04-04. Stochastic Control of Drawdowns via Reinsurance under Random Inspection. https://arxiv.org/abs/2504.03319

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