Sub-optimal investment for insurers |
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Authors: | Michele Longo Gabriele Stabile |
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Institution: | 1. Dipartimento di discipline matematiche, finanza matematica ed econometria, Università Cattolica del Sacro Cuore, Milano, Italy;2. michele.longo@unicatt.it;4. Dipartimento di Metodi e Modelli per l’Economia, il Territorio e la Finanza, Sapienza-Università di Roma, Roma, Italy |
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Abstract: | AbstractWe 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. |
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Keywords: | Insurance risk process ruin probability investment sub-optimal strategies |
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