An optimal reinsurance problem in the Cramér–Lundberg model

Cani, Arian; Thonhauser, Stefan

doi:10.1007/s00186-016-0559-8

Cited by 7 publications

(5 citation statements)

References 27 publications

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“…Since we want to use the theory of stoachstic optimal control, it is crucial to show that the value function is a solution to the problem's Hamilton-Jacobi-Bellman equation (HJB). The proof follows similar arguments as the one of Lemma 3 in Cani and Thonhauser (2017).…”

Section: Resultsmentioning

confidence: 77%

“…At this point, we can again follow the proof of Lemma 3 in Cani and Thonhauser (2017) to deduce that…”

Section: Resultsmentioning

confidence: 91%

“…Having created an analogous situation as in the proof of Lemma 3 in Cani and Thonhauser (2017), we can use the same arguments to deduce…”

Section: Resultsmentioning

confidence: 98%

“…For the latter question, the most popular choice is the ruin probability but other functionals are thinkable and interesting. For example Azcue and Muler (2005) and Cani and Thonhauser (2017) ask for the strategy maximizing a dividend payoff and it is shown that results are qualitatively different from optimal strategies for minimizing the probability of ruin. In our manuscript, we will consider a quite general selection of functionals combined in the notion of discounted penalty functions, a concept that is widely used in many branches of insurance mathematics.…”

Section: Motivationmentioning

confidence: 99%

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Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model

Preischl¹,

Thonhauser²

2019

Insurance: Mathematics and Economics

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Complementing existing results on minimal ruin probabilities, we minimize expected discounted penalty functions (or Gerber-Shiu functions) in a Cramér-Lundberg model by choosing optimal reinsurance. Reinsurance strategies are modelled as time dependant control functions, which leads to a setting from the theory of optimal stochastic control and ultimately to the problem's Hamilton-Jacobi-Bellman equation. We show existence and uniqueness of the solution found by this method and provide numerical examples involving light and heavy tailed claims and also give a remark on the asymptotics.

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Section: Resultsmentioning

confidence: 77%

“…At this point, we can again follow the proof of Lemma 3 in Cani and Thonhauser (2017) to deduce that…”

Section: Resultsmentioning

confidence: 91%

“…Having created an analogous situation as in the proof of Lemma 3 in Cani and Thonhauser (2017), we can use the same arguments to deduce…”

Section: Resultsmentioning

confidence: 98%

Section: Motivationmentioning

confidence: 99%

See 2 more Smart Citations

Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model

Preischl¹,

Thonhauser²

2019

Insurance: Mathematics and Economics

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“…Some additional results with a focus on non-proportional reinsurance contracts are given in Hipp & Taksar (2010). Recently, Cani & Thonhauser (2017) studied a dynamic reinsurance problem obtained from an economical valuation criterion in risk theory introduced by Højgaard & Taksar (1998a,b).…”

Section: Introductionmentioning

confidence: 99%

The Optimal Dynamic Reinsurance Strategies in Multidimensional Portfolio

Masoumifard¹,

Zokaei²

2020

Preprint

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The present paper addresses the issue of choosing an optimal dynamic reinsurance policy, which is state-dependent, for an insurance company that operates under multiple insurance business lines.For each line, the Cramer-Landberg model is adopted for the risk process and one of the contracts such as Proportional reinsurance, excess-of-loss reinsurance (XL) and limited XL reinsurance (LXL) is intended for transferring a portion of the risk to reinsurance. In the optimization method used in this paper, the survival function is maximized relative to the dynamic reinsurance strategies. The optimal survival function is characterized as the unique nondecreasing viscosity solution of the associated Hamilton-Jacobi-Bellman equation (HJB) equation with limit one at infinity. The finite difference method (FDM) has been utilized for the numerical solution of the optimal survival function and optimal dynamic reinsurance strategies and the proof for the convergence of the numerical solution to the survival probability function is provided. The findings of this article provide insights for the insurance companies as such that based upon the lines in which they are operating, they can choose a vector of the optimal dynamic reinsurance strategies and consequently transfer some part of their risks to several reinsurers. Using numerical examples, the significance of the elicited results in reducing the probability of ruin is demonstrated in comparison with the previous findings.

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2017

Reinsurance

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An optimal reinsurance problem in the Cramér–Lundberg model

Cited by 7 publications

References 27 publications

Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model

Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model

The Optimal Dynamic Reinsurance Strategies in Multidimensional Portfolio

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