Topic

Consistent Investment of Sophisticated Rank-Dependent Utility Agents in Continuous Time

Speaker

Hanqing JIN, Associate Professor, Mathematical Institute, University of Oxford

Host

Sang HU, Assistant Professor, School of Data Science, CUHK-Shenzhen

Date

4 September (Wednesday), 2024

Time

11:00 AM- 12:00 PM, Beijing Time

Format

Hybrid

Venue

Room 401, Dao Yuan Building

Zoom Link

https://cuhk-edu-cn.zoom.us/j/92328239059?pwd=jX7pGC8hPnp4LBmi4mphRMk73PaZJ4.1

Meeting ID: 923 2823 9059, Password: 893709

Language

English

Abstract

We study portfolio selection in a complete continuous-time market where the preference is dictated by the rank-dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the investment behavior of sophisticated consistent planners who seek (sub-game perfect) intra-personal equilibrium strategies. We provide sufficient conditions under which an equilibrium strategy is a replicating portfolio of a final wealth. We derive this final wealth profile explicitly, which turns out to be in the same form as in the classical Merton model with the market price of risk process properly scaled by a deterministic function in time. We present this scaling function explicitly through the solution to a highly nonlinear and singular ordinary differential equation, whose existence of solutions is established. Finally, we give a necessary and sufficient condition for the scaling function to be smaller than one corresponding to an effective reduction in risk premium due to probability weighting.

Biography

Prof. Jin is an Associate Professor at the Mathematical Institute and the director of Oxford-Octa Laboratory in Digital Economics.  He was an assistant professor in the National University of Singapore in 2006-2009. His general interest is in mathematical finance, behavioral finance, applied stochastic analysis, optimization, financial big data. His work focuses on the study on portfolio selection  and optimal stopping without time consistency in financial market. Recently he also worked on token economics and mathematical problems in blockchain technology.