Optimal consumption and investment with market frictions

The significant effects of market frictions on optimal consumption and investment have been widely documented throughout the literature. This dissertation devotes to address the issue when there are transaction costs in the consumption good market or when investors are subject to any combination of "absolute" and "soft" portfolio constraints. In the first paper, we examine the intertemporal optimal consumption and investment problem in a continuous-time economy with a divisible durable good. Consumption services are assumed to be proportional to the stock of the good held and adjustment of the stock is costly, in that it involves the payment of a proportional transaction cost. For the case in which the investor has an isoelastic utility function and asset prices follow a geometric Brownian motion, we establish the existence of an optimal policy and provide an explicit representation for the value function. We show that the investor acts so as to maintain the ratio of the stock of the durable to total wealth in a fixed (nonstochastic) range and that the optimal investment policy involves stochastic portfolio weights. The dependence of the optimal policies on the parameters of the model is also discussed. The second paper investigates optimal consumption and investment policies in the presence of "soft" constraints (i.e., portfolio constraints that can be violated at some costs). Examples of market frictions that can be modeled in this setting include the lack of interest on proceeds from short-sales and the differences in borrowing rates for collateralized and un-collateralized loans. Sufficient conditions for the existence of optimal policies are provided and an explicit characterization is obtained using martingale and duality techniques. This framework can be readily extended to deal with any combination of "soft" and "absolute" constraints. The third paper considers optimal consumption and investment choices and the cost of hedging contingent claims in the presence of margin requirements or, more generally, of non-linear wealth dynamics and constraints on the portfolio policies. Existence of optimal policies is established using martingale and duality techniques under general assumptions. A PDE characterization of the cost of hedging a non-negative path-independent European contingent claim is also provided.