A1122
Title: Equilibrium strategies in time-inconsistent stochastic control problems with constraints: Necessary conditions
Authors: Elisa Mastrogiacomo - Insubria University (Italy)
Marco Tarsia - Universita degli Studi dell Insubria (Italy) [presenting]
Abstract: Time-inconsistent recursive stochastic control problems are discussed, i.e., for which Bellman's principle of optimality does not hold. For this class of problems, classical optimal controls may fail to exist or to be relevant in practice, and dynamic programming is not easily applicable. Therefore, the notion of optimality is defined through a game-theoretic framework using subgame-perfect equilibrium: the preference changes are interpreted as players in a game for which a Nash equilibrium is found. The approach followed in the work relies on the Pontryagin maximum principle: the classical spike variation technique is adapted to obtain a characterization of equilibrium strategies in terms of a generalized second-order Hamiltonian function defined through pairs of BSDEs, even in the multidimensional case. It is emphasized that, similarly to the classical case, equilibrium strategies are characterized through necessary and sufficient conditions involving the Hamiltonian function. Going further, the analysis is extended to time-inconsistent recursive control problems under a constraint defined by means of an additional recursive utility under appropriate boundedness assumptions. That constraint refers to an expected value, and thus, Ekeland's variational principle is adapted to this more tricky situation. Finally, the theoretical results are applied in the financial field to finite horizon investment-consumption policies with non-exponential actualization.
