Irreversible Reinsurance: Minimization of Capital Injections in Presence of a Fixed Cost

Salvatore Federico, Giorgio Ferrari and Maria Laura Torrente
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Salvatore Federico: Center for Mathematical Economics, Bielefeld University
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
Maria Laura Torrente: Center for Mathematical Economics, Bielefeld University

No 682, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We propose a model in which, in exchange to the payment of a fixed transaction cost, an insurance company can choose the retention level as well as the time at which subscribing a perpetual reinsurance contract. The surplus process of the insurance company evolves according to the diffusive approximation of the Cramér-Lundberg model, claims arrive at a fixed constant rate, and the distribution of their sizes is general. Furthermore, we do not specify any specific functional form of the retention level. The aim of the company is to take actions in order to minimize the sum of the expected value of the total discounted flow of capital injections needed to avoid bankruptcy and of the fixed activation cost of the reinsurance contract. We provide an explicit solution to this problem, which involves the resolution of a static nonlinear optimization problem and of an optimal stopping problem for a reflected diffusion. We then illustrate the theoretical results in the case of proportional and excess-of-loss reinsurance, by providing a numerical study of the dependency of the optimal solution with respect to the model’s parameters.

Keywords: reinsurance; fixed cost; capital injections; diffusive risk model; optimal stopping (search for similar items in EconPapers)
Pages: 24
Date: 2023-10-06
New Economics Papers: this item is included in nep-rmg
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Citations: View citations in EconPapers (1)

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https://pub.uni-bielefeld.de/download/2983417/2983418 First Version, 2023 (application/pdf)

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