Subgame-perfect equilibrium strategies for time-inconsistent recursive stochastic control problems

Abstract

We study time-inconsistent recursive stochastic control problems. Since for this class of problems classical optimal controls may fail to exist or to be relevant in practice, we focus on subgame-perfect equilibrium policies. The approach followed in our work relies on the stochastic maximum principle: we adapt the classical spike variation technique to obtain a characterization of equilibrium strategies in terms of a generalized second-order Hamiltonian function defined through a pair of backward stochastic differential equations. The theoretical results are applied in the financial field to finite horizon investment-consumption policies with non-exponential actualization.