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 Cramer-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.

Longo, M., Stabile, G., Sub-optimal investment for insurers, <<COMMUNICATIONS IN STATISTICS. THEORY AND METHODS>>, 2020; 49 (17): 4298-4312. [doi:10.1080/03610926.2019.1599020] [https://hdl.handle.net/10807/134300]

Sub-optimal investment for insurers

Longo, Michele
Primo
;
2019

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 Cramer-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.
2019
Inglese
Longo, M., Stabile, G., Sub-optimal investment for insurers, <<COMMUNICATIONS IN STATISTICS. THEORY AND METHODS>>, 2020; 49 (17): 4298-4312. [doi:10.1080/03610926.2019.1599020] [https://hdl.handle.net/10807/134300]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/134300
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