Journal of Applied Mathematics and Stochastic Analysis
Volume 2007 (2007), Article ID 82753, 33 pages
Hereditary Portfolio Optimization with Taxes and Fixed Plus
Proportional Transaction Costs—Part I
Mathematics Division, US Army Research Office, P.O. Box 12211, Research Triangle Park, 27709, NC, USA
Received 23 June 2006; Revised 26 October 2006; Accepted 27 October 2006
Copyright © 2007 Mou-Hsiung Chang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This is the first of the two companion papers which treat an
infinite time horizon hereditary portfolio optimization problem in a market
that consists of one savings account and one stock account. Within the solvency region, the investor is allowed to consume from the savings account and can make transactions between the two assets subject to paying capital gain taxes as well as a fixed plus proportional transaction cost. The investor is to seek an optimal consumption-trading strategy in order to maximize the expected utility from the total discounted consumption.
The portfolio optimization problem is formulated as an infinite dimensional
stochastic classical-impulse control problem. The quasi-variational HJB inequality
(QVHJBI) for the value function is derived in this paper. The second paper contains the verification theorem for the optimal strategy. It is also shown there that the value function is a viscosity solution of the QVHJBI.