The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor α goes to zero. If uα(θ, x) denotes the optimal cost function, being the risk factor, then it is shown that limα→0αuα(θ, x) = ξ(θ) where ξ(θ) is the average on ]0, θ[ of the optimal cost of the (usual) in nite horizon risk-sensitive control problem.
Analysis | Numerical Analysis and Computation | Probability
Menaldi, JL. & Robin, M. Appl Math Optim (2005) 52: 297. doi: 10.1007/s00245-005-0829-y