A fixed-point policy-iteration-type algorithm for symmetric nonzero-sum stochastic impulse control games
arXiv:1909.03574 · doi:10.1007/s00245-020-09694-z
Abstract
Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has hindered their proliferation. Semi-analytical approaches make strong assumptions pertaining to very particular cases. To the author's best knowledge, the only numerical method in the literature is the heuristic one we put forward to solve an underlying system of quasi-variational inequalities. Focusing on symmetric games, this paper presents a simpler, more precise and efficient fixed-point policy-iteration-type algorithm which removes the strong dependence on the initial guess and the relaxation scheme of the previous method. A rigorous convergence analysis is undertaken with natural assumptions on the players strategies, which admit graph-theoretic interpretations in the context of weakly chained diagonally dominant matrices. A novel provably convergent single-player impulse control solver is also provided. The main algorithm is used to compute with high precision equilibrium payoffs and Nash equilibria of otherwise very challenging problems, and even some which go beyond the scope of the currently available theory.
arXiv comment33 pages, 9 figures, 1 table
References in corpus (6)
- Weakly chained matrices, policy iteration, and impulse control
- Convergence of implicit schemes for Hamilton-Jacobi-Bellman quasi-variational inequalities
- A fast and stable test to check if a weakly diagonally dominant matrix is a nonsingular M-matrix
- A zero-sum stochastic differential game with impulses, precommitment, and unrestricted cost functions
- Zero-sum stochastic differential game in finite horizon involving impulse controls
- A policy iteration algorithm for nonzero-sum stochastic impulse games