勷勤数学•专家报告

题      目：Portfolio Choice and Market Equilibrium under Standard of Living Preferences

报  告  人：Jeon Junkee   副教授  (邀请人：杨舟 )

                                    Kyung Hee University

时      间：7月8日  10：30-11：30

地     点：数学院西楼二楼会议室

报告人简介:

       Prof. Jeon graduated from the Department of Mathematics at Pohang University of Science and Technology with a Bachelor's degree in August 2009. He earned his Ph.D. in Financial Mathematics under the supervision of Prof. Myungjoo Kang from the Department of Mathematical Sciences at Seoul National University in August 2016. After obtaining his Ph.D., he worked as a postdoctoral researcher at the Department of Mathematical Sciences at Seoul National University for two years. Since September 2018, he has been an assistant professor (tenure-track) in the Department of Applied Mathematics at Kyung Hee University. Prof. Jeon primarily researches stochastic control problems and free boundary problems arising from optimal consumption and investment problems. His work has been published in journals such as the Journal of Economic Theory, Journal of Economic Dynamics and Control, Finance and Stochastics, and Insurance: Mathematics and Economics.

摘      要：

       We study the portfolio choice problem of an investor who has preferences for sustaining the standard of living (SLP) and investigate the equilibrium of a continuous-time pure exchange economy where a sub-population has such preferences. We show that the portfolio of an agent with SLP generates a locally constant consumption policy. In both the partial and general equilibrium, the long-term growth rates of wealth and consumption for investors with SLP align with those of investors without such preference. Additionally, we demonstrate the existence of a stationary distribution of wealth among agents in the general equilibrium, indicating that differences in standard of living preferences alone do not create a lasting mechanism for wealth inequality. Given that SLP preferences are nonconvex and non-monotone, establishing the existence of equilibrium presents significant challenges. We address the challenges by considering the individual optimization problem and showing that the individually optimal choice aligns with the socially optimal allocation. Our approach combines four methodologies, (i) the dual martingale method, (ii) transformation of the dual problem into optimal switching problems, (iii) the theory of reflected backward stochastic differential equations, and (iv) high-dimensional partial differential equation techniques.

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