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Risks 2018, 6(3), 73; https://doi.org/10.3390/risks6030073

Company Value with Ruin Constraint in Lundberg Models

Institute of Finance, Banking and Insurance, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
Received: 17 May 2018 / Revised: 27 June 2018 / Accepted: 10 July 2018 / Published: 20 July 2018
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Abstract

In this note we study the problem of company values with a ruin constraint in classical continuous time Lundberg models. For this, we adapt the methods and results for discrete de Finetti models to time and state continuous Lundberg models. The policy improvement method works also in continuous models, but it is slow and needs discretization. Better results can be obtained faster using the barrier method for discrete models which can be adjusted for Lundberg models. In this method, dividend strategies are considered which are based on barrier sequences. In our continuous state model, optimal barriers can be computed with the Lagrange method leading to a backward recursion scheme. The resulting dividend strategies will not always be optimal: in the case without ruin constraint, there are examples in which band strategies are superior. We also develop equations for optimal control of dynamic reinsurance to maximize the company value under a ruin constraint. These identify the optimal reinsurance strategy in no action regions and allow for an interactive computation of the value function. We apply the methods in a numerical example with exponential claims. View Full-Text
Keywords: stochastic control; optimal dividend payment; ruin probability constraint; Lundberg models stochastic control; optimal dividend payment; ruin probability constraint; Lundberg models
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Hipp, C. Company Value with Ruin Constraint in Lundberg Models. Risks 2018, 6, 73.

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