Asymptotic analysis for optimal investment and consumption with transaction costs with two futures contracts

We consider an agent who seeks to optimally invest and consume in the presence of proportional transaction costs. The agent can invest in two types of futures contracts, modeled as two correlated arithmetic Brownian motions, and in a money market account with constant rate of interest. She may also consume and get utility U(c) ≜cpp , c ≥ 0, where p ∈ (0, 1) and c is the rate of consumption. The agent can control the rate of consumption and influence the evolution of wealth by controlling the number of futures contracts held. Proportional transaction costs lambda i = alphailambda are charged for every trade in futures contracts of type i, i = 1, 2. All consumption is done from the money market account. The agent wishes to maximize the expected discounted integral over [0, infinity) of the utility of consumption. We compute an asymptotic expansion of the value function in powers of lambda1/3.