Optimal lifetime consumption-portfolio strategies under trading constraints and generalized recursive preferences.
The paper extends the earlier results of the same authors, concerning optimal consumption and security trading strategies of an agent with non-additive preferences, to the case of general-form convex position restrictions (including market incompleteness as a special case). To formally restate the agent's optimization problem for the trading constraint case in terms similar to the ones of the unconstrained portfolio choice problem, one needs to redefine the short risk-free interest rate process and the vector of risk prices. The most general results of the paper for the diffusion price uncertainty set-up are stated with the help of the utility gradient approach. The authors provide a characterization of the utility gradient density process. The first-order optimality conditions are obtained as a system of constrained forward-backward stochastic differential equations (FBSDE). These conditions are then simplified for homothetic recursive utilities (meaning degree-one homogeneity of the aggregator function). Then, instead of the original FBSDE system, the first-order conditions reduce to a constrained backward SDE for the Lagrange multiplier of wealth. The optimal consumption process can be characterized by an explicit SDE as well.
backward stochastic differential equation
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