報告題目：The finite-horizon consumption-investment and retirement problem with borrowing constraint
報告人：楊舟 教授 華南師範大學
報告時間：2024年9月26日 9:00-10:00
報告地點：騰訊會議 ID：941-568-357
校内聯系人：韓月才 hanyc@jlu.edu.cn
報告摘要：In this paper, we study the optimization problem of an economic agent who chooses the best time for retirement as well as consumption and investment in the presence of a mandatory retirement date. Moreover, the agent faces the borrowing constraint which is constrained in the ability to borrow against future income during working. By utilizing the dual-martingale method for the borrowing constraint, we derive a dual two-person zero-sum game between a singular-controller and a stopper over finite-time horizon. The value of the game satisfies a min-max type of parabolic variational inequality involving both obstacle and gradient constraints, which gives rise to two time-varying free boundaries that correspond to the optimal retirement and the wealth binding, respectively. Using partial differential equation (PDE) techniques, including many technical and non-standard arguments, we establish the uniqueness and existence of a strong solution to the variational inequality, as well as the monotonicity and smoothness of the two free boundaries. Furthermore, the value of game is shown to be the solution to the variational inequality, and we establish a duality theorem to characterize the optimal strategy. To the best our knowledge, this paper is the first to study the zero-sum games between a singular-controller and a stopper over finite-time horizon in the mathematical finance literature.
報告人簡介：楊舟，華南師範大學數學科學學院，教授，博士導師。主要從事金融數學和随機控制方面的研究，主要研究方向為：美式衍生産品定價、最優投資組合、最優停時問題、金融中的自由邊界問題。部分研究成果發表于MATH OPER RES、SIAM J CONTROL OPTIM、SIAM J MATH ANAL、J DIFFER EQUATIONS等期刊。曾主持五項國家基金和多項省部級基金。
