Abstract
In this article we consider the surplus process of an insurance company within the Cramér–Lundberg framework with the intention of controlling its performance by means of dynamic reinsurance. Our aim is to find a general dynamic reinsurance strategy that maximizes the expected discounted surplus level integrated over time. Using analytical methods we identify the value function as a particular solution to the associated Hamilton–Jacobi–Bellman equation. This approach leads to an implementable numerical method for approximating the value function and optimal reinsurance strategy. Furthermore we give some examples illustrating the applicability of this method for proportional and XL-reinsurance treaties.
Highlights
The determination of optimal insurance contracts is a classical topic in insurance mathematics
We will study the use of dynamic reinsurance for maximizing a particular economic performance measure which for a diffusion risk model was introduced by Højgaard and Taksar (1998a, b)
An optimal admissible reinsurance strategy u leading to the value function, i.e. a strategy which delivers the maximal return function (5)
Summary
The determination of optimal insurance contracts is a classical topic in insurance mathematics. The first paper to study dynamic optimal reinsurance in the classical risk model for the minimization of the ruin probability is Schmidli (2001), who dealt with the case of proportional reinsurance treaties This approach was extended to excess of loss contracts by Hipp and Vogt (2003). A general presentation on ruin probability minimization by means of reinsurance in the classical and diffusion risk model can be found in Schmidli (2008) This reference provides some asymptotic studies of the behaviour of optimal strategies, which in certain situations coincide with the ones maximizing the adjustment coefficient. Approach to maximize the expected utility of the surplus of an insurance company at some given deterministic terminal time by dynamic proportional reinsurance In this contribution, we will study the use of dynamic reinsurance for maximizing a particular economic performance measure which for a diffusion risk model was introduced by Højgaard and Taksar (1998a, b).
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