MOU-HSIUNG CHANG
Mathematics Division
Engineering Sciences Directorate
U. S. Army Research Office
P.O. Box 12211
Research Triangle Park, North Carolina 27709
 

HEREDITARY PORTFOLIO OPTIMIZATION WITH TRANSACTION COSTS AND
TAXES: A QUASI-VARIATIONAL HJB INEQUALITY
IN INFINITE DIMENSIONS
 
 
 

ABSTRACT

 This talk considers an infinite-time horizon portfolio optimization
problem in a market that consists of one savings account and one
stock account whose unit price satisfies a nonlinear stochastic
functional differential equation.  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-gains
taxes as well as a fixed plus proportional transaction cost.  The main objective is
to seek an optimal consumption-investment strategy in order to maximize the
expected utility from the total discounted consumption over the infinite time horizon.
The portfolio optimization problem is formulated as a stochastic control
problem that involves both the classical and impulsive controls.
A quasi-variational HJB inequality for the value function is derived and the
verification theorem for the optimal investment-consumption strategy is obtained.
The value function is also shown to be the unique viscosity solution of the HJB inequality.
 
 

***********************
MONDAY, FEBRUARY 2, 2004
212 NEW WEST
3:30 P.M.
***********************