N. G. Medhin and Lynesia Taylor.
A Portfolio Rebalancing Problem.
Dynamic Systems and Applications 30 (2021) No. 9, 1400-1419

https://doi.org/10.46719/dsa202130.09.01

ABSTRACT.
In this paper we consider a portfolio consisting of three types of assets, a bond, a liquid risky asset, and an illiquid risky asset. Liquid assets can be traded continuously whereas an illiquid asset can only be traded at specific pre-specified times or randomly. The investor’s liquid and illiquid wealth are modeled as stochastic differential equations (SDE). We consider a control problem governed by these SDEs. We will model the rebalancing of the portfolio, transferring between liquid and illiquid wealth, as an impulsive control
problem. Using a dynamic programming approach and a stochastic programming approach we will determine the the amount to transfer between the liquid and illiquid assets. Numerical examples are given to validate the correctness for our results.

AMS (MOS) Subject Classification. 91G10, 91B32, 91B10,60H30, 60H35.
Key Words and Phrases. Portfolio rebalancing, Asset allocation, HJB equation.