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Sub-optimal investment for insurers

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  • Michele Longo
  • Gabriele Stabile

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.

Suggested Citation

  • Michele Longo & Gabriele Stabile, 2020. "Sub-optimal investment for insurers," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(17), pages 4298-4312, September.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:17:p:4298-4312
    DOI: 10.1080/03610926.2019.1599020
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