Hereditary Portfolio Optimization with Taxes and Fixed PlusProportional Transaction Costs—Part I

[摘要] This is the first of the two companion papers which treat aninfinite time horizon hereditary portfolio optimization problem in a marketthat consists of onesavingsaccount and onestockaccount. Within thesolvencyregion, the investor is allowed to consume from thesavingsaccount and can make transactions between the two assets subject to paying capital gain taxes as well as a fixed plus proportional transaction cost. Theinvestoris 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 dimensionalstochastic 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.

[学科分类] 应用数学