A fully nonlinear free boundary problem for minimizing the ruin probability. (September 2020) - Guan, Chonghu
Abstract: In this paper, we consider the problem of how to run an insurance company to minimize the ruin probability in a finite time horizon. The value function v with the corresponding optimal reinsure strategy a ∗ is the solution of the following fully nonlinear equation v t − 1 2 σ 0 2 v x x + γ v x − inf 0 ≤ a ≤ 1 ( 1 2 σ 2 a 2 v x x + μ a v x ) = 0 under initial–boundary condition v ( 0, t ) = 1, v ( x, 0 ) = 0 . The main effort is to analyze the properties of the solution and the free boundary to show the optimal decision for the company.