Abstract
We consider an agent who does not consume and who invests all the wealth either (1) in a money market and in a stock market with one risky asset or (2) in a money market and takes positions in futures contracts on some asset or index. Both the trades in stock market and the changes of the position in the futures contracts are in the presence of proportional transaction costs.
We assume that the agent is interested in an integrated discounted expected utility of the wealth process over an infinite-time horizon with HARA utility function. We propose a function which assigns this value to every admissible strategy and to every initial condition provided that (1) the stock market price follows a geometric Brownian motion and (2) the futures price follows an arithmetic Brownian motion.
We show that these both cases can be treated simultaneously and that the setting of the problem leads to the explicit results that are completely analogical.