Smooth Value Function with Applications in Wealth-CVaR Efficient Portfolio and Turnpike Property

TL;DR

This paper extends the analysis of utility functions in portfolio optimization, providing explicit solutions for wealth-CVaR trade-offs and demonstrating the turnpike property for long-term investors.

Contribution

It generalizes previous results to broader utility functions and offers explicit control strategies for wealth-CVaR optimization and long-term investment behavior.

Findings

Explicit optimal control for wealth-CVaR frontier

Positive correlation between wealth and CVaR

Proof of turnpike property for long-run investors

Abstract

In this paper we continue the study of Bian-Miao-Zheng (2011) and extend the results there to a more general class of utility functions which may be bounded and non-strictly-concave and show that there is a classical solution to the HJB equation with the dual control method. We then apply the results to study the efficient frontier of wealth and conditional VaR (CVaR) problem and the turnpike property problem. For the former we construct explicitly the optimal control and discuss the choice of the optimal threadshold level and illustrate that the wealth and the CVaR are positively correlated. For the latter we give a simple proof to the turnpike property of the optimal policy of long-run investors and generalize the results of Huang-Zariphopoulou (1999).