Optimal Consumption Until Ruin for an Endowment Described by an Autonomous ODE for an Infinite Time Horizon

• 成果类型: Article
• 署名作者: Grandits, Peter
• 署名单位: Technische Universitat Wien
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2015.0763
• 发表日期: 2016
• 页码: 953-968
• 关键词: uniqueness

摘要

We give an algorithmic solution of the optimal consumption problem sup(C) integral([0, tau]) e(-beta t) dC(t), where C-t denotes the accumulated consumption until time t, and tau denotes the time of ruin. Moreover, the endowment process X-t is modeled by X-t = x + integral(t)(0) mu(X-s) ds - C-t. We solve the problem by showing that the function provided by the algorithm solves the Hamilton-Jacobi (HJ) equation in a viscosity sense and that the same is true for the value function of the problem. The argument is finished by a uniqueness result. It turns out that one has to change the optimal strategy at a sequence of endowment values, described by a free boundary value problem. Finally we give an illustrative example.