勷勤数学•专家报告

题      目：Consumption and  Portfolio Choice with Costly Adjustment for Living Standards

报  告  人：温焕尧 教授  (邀请人：喻洪俊)

                                   华南理工大学

时      间：4月23日  14：40-15：40

地     点：数科院东楼401

报告人简介:

       温焕尧，华南理工大学数学学院教授、博士生导师、院长。目前担任广东省青年科学家协会副会长和华南理工大学党外知识分子联席会副会长。主要从事流体力学中的偏微分方程的数学理论研究。研究成果发表在Adv. Math.、Arch. Rational Mech. Anal.、CVPDEs、J. Functional Analysis、J.  Math. Pures Appl.、 Math. Models Meth. Appl. Sci.、SIAM J. Math. Anal.等杂志。先后主持国家自然科学基金青年项目、面上项目和优秀青年科学基金项目。2016-2019年获聘广东省青年珠江学者。

摘      要：

       We study a finite-horizon consumption and portfolio choice problem incorporating adjustment costs for living standards, with a focus on older individuals. The optimal strategies differ notably between individuals with moderate  and high wealth: ordinary individuals reduce consumption and exhibit increasing relative risk aversion, while wealthy individuals increase consumption and exhibit decreasing relative risk aversion until a critical time, after which they shift entirely to safe assets. Our main technical contribution lies in solving this problem via a novel synthesis of four methodologies: the dual martingale approach, transformation into optimal switching problems, partial       differential equation techniques—focusing on double obstacle problems—and the Skorokhod lemma.

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