Optimal Insurance with Limited Commitment in a Finite Horizon

• Tác giả: Junkee Jeon, Hyeng Keun Koo, Kyunghyun Park
• Ngôn ngữ: eng
• Ký hiệu phân loại: 174.9368 Other professions and occupations
• Thông tin xuất bản: 2018
• Bộ sưu tập: Metadata
• ID: 162512

Tóm tắt

Comment: 44pages, 7 figuresWe study a finite horizon optimal contracting problem of a risk-neutral principal and a risk-averse agent who receives a stochastic income stream when the agent is unable to make commitments. The problem involves an infinite number of constraints at each time and each state of the world. Miao and Zhang (2015) have developed a dual approach to the problem by considering a Lagrangian and derived a Hamilton-Jacobi-Bellman equation in an infinite horizon. We consider a similar Lagrangian in a finite horizon, but transform the dual problem into an infinite series of optimal stopping problems. For each optimal stopping problem we provide an analytic solution by providing an integral equation representation for the free boundary. We provide a verification theorem that the value function of the original principal's problem is the Legender-Fenchel transform of the integral of the value functions of the optimal stopping problems. We also provide some numerical simulation results of optimal contracting strategies