The finite-horizon consumption-investment and retirement problem with borrowing constraint
報(bào)告人簡(jiǎn)介：楊舟，華南師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院，教授，博士導(dǎo)師。主要從事金融數(shù)學(xué)和隨機(jī)控制方面的研究，主要研究方向?yàn)椋好朗窖苌a(chǎn)品定價(jià)、最優(yōu)投資組合、最優(yōu)停時(shí)問(wèn)題、金融中的自由邊界問(wèn)題。部分研究成果發(fā)表于MATH OPER RES、SIAM J CONTROL OPTIM、SIAM J MATH ANAL、J DIFFER EQUATIONS等期刊。曾主持五項(xiàng)國(guó)家基金和多項(xiàng)省部級(jí)基金。
報(bào)告內(nèi)容介紹：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.
