A fully nonlinear free boundary problem for minimizing the ruin probability. (September 2020)

• Record Type: Journal Article
• Authors: Guan, Chonghu
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 35R35 -- 91B70 -- 93E20; Parabolic fully nonlinear equation -- Free boundary -- Stochastic optimal control -- Controllable risk -- Reinsurance -- Ruin probability; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111924
• Languages: English
• ISSNs: 0362-546X

Abstract

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.