Risk-sensitive and Mean Variance Optimality in Continuous-time Markov Decision Chains

0493556 - ÚTIA 2019 RIV CZ eng K - Conference Paper (Czech conference)
Sladký, Karel
Risk-sensitive and Mean Variance Optimality in Continuous-time Markov Decision Chains.
36th International Conference Mathematical Methods in Economics. Praha: MatfyzPress, 2018 - (Váchová, L.; Kratochvíl, V.), s. 497-512. ISBN 978-80-7378-371-6.
[36th International Conference Mathematical Methods in Economics. Jindřichův Hradec (CZ), 12.09.2018-14.09.2018]
R&D Projects: GA ČR GA18-02739S
Institutional support: RVO:67985556
Keywords : continuous-time Markov decision chains * exponential utility functions * certainty equivalent * mean-variance optimality * connections between risk-sensitive and risk-neutral optimality
OECD category: Economic Theory
http://library.utia.cas.cz/separaty/2018/E/sladky-0493556.pdf

In this note we consider continuous-time Markov decision processes with finite state and actions spaces where the stream of rewards generated by the Markov processes is evaluated by an exponential utility function with a given risk sensitivitycoefficient (so-called risk-sensitive models). If the risk sensitivity coefficient equals zero (risk-neutral case) we arrive at a standard Markov decision process. Then we can easily obtain necessary and sufficient mean reward optimality conditions and the variability can be evaluated by the mean variance of total expected rewards. For the risk-sensitive case, i.e. if the risk-sensitivity coefficient is non-zero, for a given value of the risk-sensitivity coefficient we establish necessary and sufficient optimality conditions for maximal (or minimal) growth rate of expectation of the exponential utility function, along with mean value of the corresponding certainty equivalent. Recall that in this case along with the total reward also its higher moments are taken into account.
Permanent Link: http://hdl.handle.net/11104/0286979