Utility Maximization Trading Two Futures with Transaction Cost

An agent invests in two types of futures contracts, whose prices are possibly correlated arithmetic Brownian motions, and invests in a money market account with a constant interest rate. The agent pays a transaction cost for trading in futures proportional to the size of the trade. She also receives utility from consumption. The agent maximizes expected infinite-horizon discounted utility from consumption. We determine the first two terms in the asymptotic expansion of the value function in the transaction cost parameter around the known value function for the case of zero transaction cost. The method of solution when the futures are uncorrelated follows a method used previously to obtain the analogous result for one risky asset. However, when the futures are correlated, a new methodology must be developed. It is suspected in this case that the value function is not twice continuously differentiable, and this prevents application of the former methodology.