2007/01/01 by Harold J. Kushner · 1 voice
Economics, Econometrics and Finance · Social Sciences · #Climate Change Policy and Economics #Insurance, Mortality, Demography, Risk Management #Stochastic processes and financial applications
paper · doi:10.1137/050647931
openalex publication_date 2007/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/16
The Markov chain approximation method is a widely used and efficient family of methods for the numerical solution of many types of stochastic control problems in continuous time for reflected-jump-diffusion–type models. It converges under broad conditions, and it has been extended to zero-sum stochastic differential games. We apply the method to a class of nonzero stochastic differential games with a diffusion system model where the controls for the two players are separated in the dynamics and cost function. There have been successful applications of the algorithms, but convergence proofs have been lacking. It is shown that equilibrium values for the approximating chain converge to equilibrium values for the original process and that any equilibrium value for the original process can be approximated by an ε-equilibrium for the chain for arbitrarily small ε > 0. The numerical method solves a stochastic game for a finite-state Markov chain.