Paper Info
Title
Global Closed-form Approximation of Free Boundary for Optimal Investment Stopping Problems.
Abstract
In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a fully nonlinear partial differential equation. Using the dual control method, we derive the asymptotic properties of the dual value function and the associated dual free boundary for a class of utility functions, including power and non-hyperbolic absolute risk aversion utilities. We construct a global closed-form approximation to the dual free boundary, which greatly reduces the computational cost. Using the duality relation, we find the approximate formulas for the optimal value function, trading strategy, and exercise boundary for the optimal investment stopping problem. Numerical examples show the approximation is robust, accurate, and fast.
Year
DOI
Venue
2019
10.1137/18M1184850
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
Field
DocType
optimal investment stopping problem,dual control method,free boundary,global closed-form approximation
Trading strategy,Mathematical optimization,Optimal control,Optimal stopping,Horizon,Bellman equation,Utility maximization problem,Free boundary problem,Duality (optimization),Mathematics
Journal
Volume
Issue
ISSN
57
3
0363-0129
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Jingtang Ma112012.98
Jie Xing201.69
Harry Zheng3289.30