[00143] Recent advances in stochastic optimal control and contract theory
Session Time & Room : 5D (Aug.25, 15:30-17:10) @D501
Type : Proposal of Minisymposium
Abstract : The aim of this session is to bring together some of the most active junior researchers in the areas of stochastic optimal control, with an emphasis on applications to contract theory and principal-agent problems. It will be a perfect and timely opportunity to take stock of the recent progresses in these very trendy topics, as well as to highlight the deep links that they share. In particular, a specific attention will be put on relationships with mean- field and Stackelberg games, McKean-Vlasov optimal control, and time-inconsistent optimal control problems.
Organizer(s) : Dylan Possamaï
Sponsor : This session is sponsored by the SIAM Activity Group on Financial Mathematics and Engineering.
[00182] Mean field optimal stopping and applications in contract theory
Author(s) :
Mehdi Christian Talbi (ETH Zurich)
Thibaut Mastrolia (UC Berkeley)
Abstract : Mean field optimal stopping problems correspond to optimization problems where a central planner controls a distribution of interacting agents by assigning each of them a stopping time. After explaining how these problems can be studied through dynamic programming, we propose an application to contract theory: one Principal proposes contracts to interacting Agents, and each contract includes a continuous payment and a retirement time, which leads the Principal to solve a mixed control-and-stopping mean field problem.
[00242] A stochastic target approach to Stackelberg games and moral hazard with constraints
Author(s) :
Emma Hubert (Princeton University)
Abstract : In this talk, we provide a unifying framework for Stackelberg games and principal-agent problems with moral hazard and constraints on the terminal payment. The main idea is that this type of problems can be reformulated as more standard control problems with stochastic target. Indeed, the agent’s problem can be rewritten as a BSDE, controlled by the principal, and then the constraint on the terminal payment is equivalent to a terminal constraint on this controlled process.
[05385] Asset Bubble Riding with Price-Dependent Entry: a Mean Field Game of Controls with Common Noise
Author(s) :
Dylan Possamaï (ETH Zürich)
Shichun Wang (Princeton University)
Abstract : In this talk, we present an existence result for mean field games of controls with common noise and random entry time. We obtain an equilibrium by first solving discretized versions of the game in the weak formulation and examining the measurability property in the limit. As a motivating example, we extend the existing game-theoretic model on optimal execution in the presence of an asset bubble by allowing for price-dependent entry times. Agents are characterized by their individual entry thresholds that represent their beliefs in the strength of the bubble. Conversely, the growth dynamics of the bubble is fueled by the influx of players. On top of the asset price, a second source of common noise is the exogenous bubble burst time, which we incorporate into the model via progressive enlargement of filtration. In the end, we show the equilibrium strategy can be decomposed into before-and-after-burst segments, each part containing only the market information.
[05410] Bubble Riding with Price-Dependent Entry: Mean Field Games of Controls with Common Noise
Author(s) :
Ludovic Tangpi (Princeton University)
Shichun Wang (Princeton University)
Abstract : In this talk, we present an existence result for mean field games of controls with common noise and random entry time. We obtain an equilibrium by first solving discretized versions of the game in the weak formulation and examining the measurability property in the limit. As a motivating example, we extend the existing game-theoretic model on optimal execution in the presence of an asset bubble by allowing for price-dependent entry times. Agents are characterized by their individual entry thresholds that represent their beliefs in the strength of the bubble. Conversely, the growth dynamics of the bubble is fueled by the influx of players. On top of the asset price, a second source of common noise is the exogenous bubble burst time, which we incorporate into the model via progressive enlargement of filtration. In the end, we show the equilibrium strategy can be decomposed into before-and-after-burst segments, each part containing only the market information.
