Dynamic Portfolio Theory and Risk Aversion

This chapter presents a theory of optimal lifetime consumption-portfolio choice in a continuous information setting, with emphasis on the modeling of risk aversion through generalized recursive utility. A novel contribution is a decision theoretic development of the notions of source-dependent first or second order risk aversion. Backward Stochastic Differential Equations (BSDEs) are explained heuristically as continuous-information versions of backward recursions on an information tree, and are used to formulate utility functions as well as optimality conditions. The role of scale invariance and quadratic BSDEs in obtaining tractable solutions is explained. A final section outlines extensions, including optimality conditions under trading constraints, and tractable formulations with nontradeable income.