Nonlocality, Nonlinearity, and Time Inconsistency in Stochastic Differential Games
arXiv:2112.14409 · doi:10.1111/mafi.12420
Abstract
This paper proves the existence and uniqueness results (in the sense of maximally defined regularity) as well as the stability analysis for the solutions to a class of nonlocal fully-nonlinear parabolic systems, where the nonlocality stems from the flow feature (controlled by an external temporal parameter) of the systems. The derived mathematical results generalize the theory of stochastic differential games to incorporate with behavioral factors such as time-inconsistent preferences, which facilitate developments of many studies in financial economics including robust stochastic controls and games under relative performance concerns. Moreover, with the well-posedness results, we establish a general multidimensional Feynman--Kac formula in the presence of nonlocality (time inconsistency).
arXiv commentarXiv admin note: text overlap with arXiv:2110.04237
References in corpus (5)
- Being serious about non-commitment: subgame perfect equilibrium in continuous time
- Extended backward stochastic Volterra integral equations and their applications to time-inconsistent stochastic recursive control problems
- A regular equilibrium solves the extended HJB system
- Small-time solvability of a flow of forward-backward stochastic differential equations
- Present-Biased Lobbyists in Linear Quadratic Stochastic Differential Games