2017/08/08 by Juan Li, Li, Juan, Nana Zhao +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1708.02335
openalex publication_date 2017/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In ergodic stochastic problems the limit of the value function Vλ of the associated discounted cost functional with infinite time horizon is studied, when the discounted factor λ tends to zero. These problems have been well studied in the literature and the used assumptions guarantee that the value function λVλ converges uniformly to a constant as λ→ 0. The objective of this work consists in studying these problems under assumptions, namely, the nonexpansivity assumption, under which the limit function is not necessarily constant. Our discussion goes beyond the case of the stochastic control problem with infinite time horizon and discusses also Vλ given by a Hamilton-Jacobi-Bellman equation of second order which is not necessarily associated with a stochastic control problem. On the other hand, the stochastic control case generalizes considerably earlier works by considering cost functionals defined through a backward stochastic differential equation with infinite time horizon and we give an explicit representation formula for the limit of λVλ, as λ→ 0.