Optimal discounted drawdowns in a diffusion approximation under proportional reinsurance. (30th June 2022)

• Record Type: Journal Article
• Authors: Brinker, Leonie Violetta; Schmidli, Hanspeter
• Is Part Of: Journal of applied probability. Volume 59:Number 2(2022)
• Page Start: 527
• Page End: 540
• Publication Date: 2022-06-30
• Subjects: Drawdown -- diffusion approximation -- optimal proportional reinsurance -- Hamilton–Jacobi–Bellman equation; 91G05 -- 93E20 -- 60G44 -- 60J60; 519.2
• DOI: 10.1017/jpr.2021.68
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: A diffusion approximation to a risk process under dynamic proportional reinsurance is considered. The goal is to minimise the discounted time in drawdown; that is, the time where the distance of the present surplus to the running maximum is larger than a given level $d > 0$ . We calculate the value function and determine the optimal reinsurance strategy. We conclude that the drawdown measure stabilises process paths but has a drawback as it also prevents surpassing the initial maximum. That is, the insurer is, under the optimal strategy, not interested in any more profits. We therefore suggest using optimisation criteria that do not avoid future profits.