大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Time-inconsistent control and backward integral Volterra SDEs

Dylan Possamaï (ETH Zürich)

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大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第119回

Time-inconsistent control and backward integral Volterra SDEs

Dylan Possamaï (ETH Zürich)

This paper is the first attempt at a general non-Markovian theory of time-inconsistent stochastic control problems in continuous-time. We consider sophisticated agents who are aware of their time-inconsistency and take into account in future decisions. We prove here that equilibria in such a problem can be characterised through a new type of multi-dimensional system of backward SDEs, for which we obtain wellposedness. Unlike the existing literature, we can treat the case of non-Markovian dynamics, and our results go beyond verification type theorems, in the sense that we prove that any equilibrium must necessarily arise from our system of BSDEs. If time permits, an application to contract theory will be presented, thus highlighting a potential fruitful link with BSVIEs. This is a joint work with Camilo Hernández, Columbia University.