6 research outputs found
Continuous-time Markov decision processes under the risk-sensitive average cost criterion
This paper studies continuous-time Markov decision processes under the
risk-sensitive average cost criterion. The state space is a finite set, the
action space is a Borel space, the cost and transition rates are bounded, and
the risk-sensitivity coefficient can take arbitrary positive real numbers.
Under the mild conditions, we develop a new approach to establish the existence
of a solution to the risk-sensitive average cost optimality equation and obtain
the existence of an optimal deterministic stationary policy.Comment: 14 page
Markov Decision Processes with Risk-Sensitive Criteria: An Overview
The paper provides an overview of the theory and applications of
risk-sensitive Markov decision processes. The term 'risk-sensitive' refers here
to the use of the Optimized Certainty Equivalent as a means to measure
expectation and risk. This comprises the well-known entropic risk measure and
Conditional Value-at-Risk. We restrict our considerations to stationary
problems with an infinite time horizon. Conditions are given under which
optimal policies exist and solution procedures are explained. We present both
the theory when the Optimized Certainty Equivalent is applied recursively as
well as the case where it is applied to the cumulated reward. Discounted as
well as non-discounted models are reviewe
Exit Time Risk-Sensitive Control for Systems of Cooperative Agents
We study sequences, parametrized by the number of agents, of many agent exit
time stochastic control problems with risk-sensitive cost structure. We
identify a fully characterizing assumption, under which each of such control
problem corresponds to a risk-neutral stochastic control problem with additive
cost, and sequentially to a risk-neutral stochastic control problem on the
simplex, where the specific information about the state of each agent can be
discarded. We also prove that, under some additional assumptions, the sequence
of value functions converges to the value function of a deterministic control
problem, which can be used for the design of nearly optimal controls for the
original problem, when the number of agents is sufficiently large
Exit time risk-sensitive stochastic control problems related to systems of cooperative agents
We study sequences, parametrized by the number of agents, of exit time stochastic control problems with risk-sensitive costs structures generate by unbounded costs. We identify a fully characterizing assumption, under which, each of them corresponds to a risk-neutral stochastic control problem with additive cost, and also to a risk-neutral stochastic control problem on the simplex, where the specific information about the state of each agent can be discarded. We finally prove that, under some additional assumptions, the sequence of value functions converges to the value function of a deterministic control problem