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- W113456011 abstract "We model the reserve of an insurance company as a Cramer-Lundberg process. We assume that the management has the possibility of investing part of its reserve in a non-liquid asset while the rest is invested in a liquid one. The goal is to minimize the ruin probability of the company. We assume that the yield of the non-liquid asset is greater than the one of the liquid asset but there is a transaction cost for selling immediately the non-liquid asset. Our aim is to find a dynamic choice of the amounts of the reserve invested in the liquid and in the non-liquid asset. We characterize the optimal value function as the viscosity solution of the associated Hamilton-Jacobi-Bellman equation. This equation is a two-dimensional first order non linear integro-differential equation leading to a free boundary problem. The optimal choice of the amounts invested in the liquid and in the non-liquid asset is specified by the so called region of inaction. Inside the region of inaction, the reserve invested in the non-liquid asset should not change, and outside this region the management should invest immediately a positive amount of the reserve in the non-liquid asset. In the case of exponential claim distributions we characterize the region of inaction for the optimal strategy and obtain the optimal ruin probability. We obtain the optimal ruin probability for exponential claim distributions, and we characterize the region of inaction for the optimal strategy." @default.
- W113456011 created "2016-06-24" @default.
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- W113456011 date "2008-01-01" @default.
- W113456011 modified "2023-09-27" @default.
- W113456011 title "Minimizing ruin probability in the presence of a non-liquid investment" @default.
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