Sub-optimal investment for insurers

Michele Longo and Gabriele Stabile

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 17, 4298-4312

Abstract: We consider the investment problem for a non-life insurance company seeking to minimize the ruin probability. Its reserve is described by a perturbed risk process possibly correlated with the financial market. Assuming exponential claim size, the Hamilton-Jacobi-Bellman equation reduces to a first order nonlinear ordinary differential equation, which seems hard to solve explicitly. We study the qualitative behavior of its solution and determine the Cramér-Lundberg approximation. Moreover, our approach enables to find very naturally that the optimal investment strategy is not constant. Then, we analyze how much the company looses by adopting sub-optimal constant (amount) investment strategies.

Date: 2020
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DOI: 10.1080/03610926.2019.1599020

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