LINKED RECURSIVE PREFERENCES AND OPTIMALITY

Abstract

We study a class of optimization problems involving linked recursive preferences in a continuous-time Brownian setting. Such links can arise when preferences depend directly on the level or volatility of wealth, in principal-agent (optimal compensation) problems with moral hazard, and when the impact of social influences on preferences is modeled via utility (and utility diffusion) externalities. We characterize the necessary first-order conditions, which are also sufficient under additional conditions ensuring concavity. We also examine applications to optimal consumption and portfolio choice, and applications to Pareto optimal allocations. We study a class of optimization problems involving linked recursive preferences in a continuous-time Brownian setting. Such links can arise when preferences depend di- rectly on the level or volatility of wealth, in principal-agent (optimal compensation) problems with moral hazard, and when the impact of social influences on preferences is modeled via utility (and utility diffusion) externalities. We characterize the necessary first-order conditions (FOCs), which are also sufficient under additional conditions en- suring concavity. We also examine applications to optimal consumption and portfolio choice, and applications to Pareto optimal allocations. The optimization problems we study all reduce to maximizing a linear combination of a multidimensional backward stochastic differential equation (BSDE) system. This BSDE system was proposed by El Karoui, Peng, and Quenez (1997) as an extension of Duffie and Epstein's (1992) stochastic differential utility (SDU). Lazrak and Quenez (2003) show, in the single-agent (one-dimensional) case, that this recursive specification allows considerable flexibility in separately modeling risk aversion and intertemporal substitution, and unifies many preference classes including SDU and multiple-prior formulations (Maenhout 1999; Anderson, Hansen, and Sargent 2000; Chen and Epstein 2002). We show that the multidimensional analog can be used to model preferences in which wealth or wealth diffusion enter the aggregators, preferences in which social influences are modeled through the dependence of each agent's aggregator on utility or risk levels (or utility diffusions) of other agents, and preferences in principal/agent This paper is dedicated to Stephanie Schroder, who edited earlier versions of this paper. We benefited from the many helpful suggestions of the anonymous referees and the Associate Editor. Manuscript received September 2011; final revision received April 2013.