On the Maximization of Long-Run Conditional Value-at-Risk for Markov Decision Processes

Optimizing Risk-Seeking Sequential Decisions via Conditional Value-at-Risk Decision makers may exhibit risk-seeking preferences in finance, energy operations, and stochastic resource management, yet corresponding Markov decision process (MDP) theories remain underdeveloped. In this paper, “On the Maximization of Long-Run CVaR for Markov Decision Processes,” Xia, Yu, and Wu investigate infinite-horizon MDPs maximizing long-run conditional value-at-risk (CVaR) for instantaneous rewards. They prove optimality for stationary randomized policies and show deterministic policies may fail; an optimal policy randomizes over at most two actions. By converting the original problem into a minimax saddle point formulation, the authors develop solvable linear programming and globally convergent gradient descent algorithms. Results are further extended to joint mean-CVaR optimization and validated on real-world microgrid scheduling data. This work fills gaps for risk-seeking MDPs and delivers practical computation tools for tail-oriented sequential decision making.