Dear Colleagues,

On March 29, 2023, 13:00-14:00, Dr. Marco Tarsia (University of Insubria) will give a talk on “Subgame-perfect equilibrium strategies for time-inconsistent recursive stochastic control problems” (joint work with Elisa Mastrogiacomo).

The seminar will be held in person and online via the MS Teams platform.

Link: https://teams.microsoft.com/l/meetup-join/19%3ameeting_OWU0MDRiNjctYWNmYS00M...

Place: Dipartimento di Economia, Via Monte Generoso 71, room TBA.

Below you can find an abstract of Marco’s talk. You are all invited.

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Abstract

In this talk, we discuss about time-inconsistent recursive stochastic control problems, i.e., for which Bellman’s principle of optimality does not hold. In practice, a restriction of an optimal control for a specific initial pair on a later time interval might not be optimal for that corresponding initial pair; this happens, for instance, in dynamic utility maximization problems for investment- consumption strategies under non-exponential discounting. 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 by means of subgame-perfect equilibrium: we interpret our preference changes which, realistically, are inconsistent over time, as players in a game for which we want to find a Nash equilibrium. The approach followed in our work relies on the stochastic (Pontryagin) 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 pairs of backward stochastic differential equations, even in the multidimensional case. We emphasize that, similarly to the classical case, equilibrium strategies are characterized through both a necessary condition and a sufficient condition involving the generalized Hamiltonian function, whereas, contrary to the classical case, this sufficient condition works even in the absence of extra convexity assumptions. Going further, our analysis is extended to time-inconsistent recursive stochastic 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 so we adapt Ekeland’s variational principle to this trickier situation. Finally, the theoretical results are applied in the financial field to finite horizon investment-consumption policies with non-exponential actualization. Here the existence of non-trivial equilibrium policies is also ascertained.

Best regards,

Elisa Mastrogiacomo ----------------------------------------- Professore Associato di Metodi matematici dell'economia e delle scienze attuariali e finanziarie DIPARTIMENTO D'ECCELLENZA 2023/2027 Università degli Studi dell'Insubria Dipartimento di Economia

Via Monte Generoso, 71 – 21100 Varese tel. +39 0332/395528

web: www.uninsubria.ithttp://www.uninsubria.it/ mail: elisa.mastrogiacomo@uninsubria.itmailto:mario.rossi@uninsubria.it

Chiaramente Insubria!

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