2023/06/25 by Łukasz Stettner, Stettner, Łukasz · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #60J20 #90C40 #93E20 #Decision-Making and Behavioral Economics #Discounting #Econometrics #Economic theories and models #Economics #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Mathematics #Microeconomics #Optimization and Control (math.OC) #Time preference
paper · pdf · doi:10.48550/arxiv.2306.14224
openalex publication_date 2023/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Controlled discrete time Markov processes are studied first with long run general discounting functional. It is shown that optimal strategies for average reward per unit time problem are also optimal for average generally discounting functional. Then long run risk sensitive reward functional with general discounting is considered. When risk factor is positive then optimal value of such reward functional is dominated by the reward functional corresponding to the long run risk sensitive control. In the case of negative risk factor we get an asymptotical result, which says that optimal average reward per unit time control is nearly optimal for long run risk sensitive reward functional with general discounting, assuming that risk factor is close to 0. For this purpose we show in Appendix upper estimates for large deviations of weighted empirical measures, which are of independent interest.