MFGs for partially reversible investment

A Stochastic Partially Reversible Investment Problem on a Finite Time-Horizon: Free-Boundary Analysis

We study a continuous-time, finite horizon, stochastic partially reversible investment problem for a firm producing a single good in a market with frictions. The production capacity is modeled as a one-dimensional, time-homogeneous, linear diffusion controlled by a bounded variation process which represents the cumulative investment-disinvestment strategy. We associate to the investment-disinvestment problem a zero-sum optimal stopping game and characterize its value function through a free-boundary problem with two moving boundaries. These are continuous, bounded and monotone curves that solv…

Signatured Deep Fictitious Play for Mean Field Games with Common Noise

Existing deep learning methods for solving mean-field games (MFGs) with common noise fix the sampling common noise paths and then solve the corresponding MFGs. This leads to a nested-loop structure with millions of simulations of common noise paths in order to produce accurate solutions, which results in prohibitive computational cost and limits the applications to a large extent. In this paper, based on the rough path theory, we propose a novel single-loop algorithm, named signatured deep fictitious play, by which we can work with the unfixed common noise setup to avoid the nested-loop struct…

具有终端状态约束的平均场博弈

Mean field games with terminal state constraints

研究具有终端状态约束的平均场博弈，通过条件McKean-Vlasov型正倒向随机微分方程刻画解，并证明线性情形下解的存在唯一性及Lasry-Lions唯一性。

带约束奇异控制的平稳遍历平均场博弈

Stationary Ergodic Mean-field Games of Constrained Singular Controls

该研究针对带约束奇异控制的平稳遍历平均场博弈，推导了泊松阈值奇异控制的平稳分布，证明了平稳平均场均衡的存在唯一性，为相关投资案例研究提供了易处理框架。