Investment-Consumption Models with Transaction Fees and Markov-Chain Parameters

Abstract

This paper considers an infinite horizon investment-consumption model in which a single agent consumes and distributes his wealth in two assets, a bond and a stock. The problem of maximization of the total utility from consumption is treated. State (amount allocated in assets) and control (consumption, rates of trading) constraints are present. It is shown that the value function is the unique viscosity solution of a system of variational inequalities with gradient constraints.