State-Dependent Utilities and Incomplete Markets

The problem of optimal consumption and investment for an agent that does not influence the market is solved. The optimization criteria are based on a state-dependent utility functional as proposed in Londoño (2009). The proposed solution is given in any market without state-tame arbitrage opportunities, includes several utilities structures, and includesincomplete marketswhere there are multiple state variables. The solutions obtained for optimal wealths consumptions, and portfolios are explicit and easily computable; the main condition for the result to hold is that the income process of each agent is hedgeable, requiring a natural condition on employer and employee to agree on a contract whose risk can be managed by both parties. In this paper we also developed a theory of markets when the processes are generalization of Brownian flows on manifolds, since this framework shows to be the natural one whenever the problem of intertemporal equilibrium is addressed.