Constrained utility deviation-risk optimization and time-consistent HJB equation
File(s)
Accepted version
Author(s)
Zheng, Harry
gu, jiawen
Si, Shijing
Type
Journal Article
Abstract
In this paper we propose a unified utility deviation-risk model which covers both utilitymaximization and mean-variance analysis as special cases. We derive the time-consistentHamilton-Jacobi-Bellman (HJB) equation for the equilibrium value function and significantlyreduce the number of state variables, which makes the HJB equation derived in this papermuch easier to solve than the extended HJB equation in the literature. We illustrate theusefulness of the time-consistent HJB equation with several examples which recover theknown results in the literature and go beyond, including mean-variance model with stochasticvolatility dependent risk aversion, utility deviation-risk model with state dependent riskaversion and control constraint, and constrained portfolio selection model. The numericaland statistical tests show that the utility and deviation-risk have significant impact on theequilibrium control strategy and the distribution of the terminal wealth.
Date Issued
2020-03-23
Date Acceptance
2020-01-22
Citation
SIAM Journal on Control and Optimization, 2020, 58 (2), pp.866-894
ISSN
0363-0129
Publisher
Society for Industrial and Applied Mathematics
Start Page
866
End Page
894
Journal / Book Title
SIAM Journal on Control and Optimization
Volume
58
Issue
2
Copyright Statement
© 2020, Society for Industrial and Applied Mathematics
Subjects
Science & Technology
Technology
Physical Sciences
Automation & Control Systems
Mathematics, Applied
Mathematics
utility deviation-risk optimization
stochastic risk aversion
incomplete market
control constraint
time-consistent dynamic programming equation
VARIANCE PORTFOLIO SELECTION
CONSUMPTION
CHOICE
0102 Applied Mathematics
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Industrial Engineering & Automation
Publication Status
Published
Date Publish Online
2020-03-23