Prin2022 Stochastic Control & Games and the role of information

Prin 2022

Stochastic Control & Games and the role of information

Project Description

The project focuses on stochastic optimization problems and games with a special emphasis on the role of information and other non-standard features such as time-inconsistency, impulse controls or singular controls. In standard stochastic control and games, agents are usually assumed to have complete knowledge of the state variables and often, for mathematical tractability, of the driving noise. When we think of applications in various social sciences (e.g., economics, finance, insurance) such an assumption is very questionable, hence it is important to go beyond that by considering, e.g., agents having different sources of information or limited knowledge of the state variables. This creates new challenges from a theoretical as well as an applied perspective, that we want to tackle within this project.

The proposal is structured into three main parts: the first one on single agent optimization problems, i.e., stochastic control; the second one on stochastic differential games for a small or a very large population of players as in mean-field games (MFGs); the third part instead gathers applications, mainly in economics, finance and insurance, that we will explore and develop during the project.

This is a 2 year project starting on September 29, 2023 and funded by MUR - Italian Ministry of Universities and Research

WP 1: Single-agent optimization problems

We deal with two main classes of problems: (1) stochastic control problems with partial information where the optimizer has only limited knowledge of the surrounding environment, leading to the use of filtering theory in order to estimate non-observable state variables following suitable jump-diffusion dynamics; (2) optimization problems for a time-inconsistent agent (so-called behavioural agent), where the dynamic programming principle cannot be used, and various notions of optimality must be developed and exploited.

WP 2: Multi-agent optimization problems

We extend our analysis by including strategic interaction among several players and consider two kinds of game: (1) Dynkin and impulse games with asymmetric information, i.e., games where players decide to stop (Dynkin games) or to induce jumps in the state variable (impulse games) at strategically chosen times, and in which players have different sources of information; (2) Mean-field games, i.e., limit of symmetric stochastic differential games for a large population of players, where a notion more general than Nash equilibrium will be addressed in full.

WP 3: Applications

We investigate a series of important applications spanning macroeconomics, finance, insurance and energy markets. We will apply and suitably specialize the theoretical frameworks developed in parts 1 and 2 to solve and analyze in depth models motivated by concrete problems in those diverse fields.

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