Existence and Finiteness Conditions for Risk-Sensitive Planning: Results
  and Conjectures
  Decision-theoretic planning with risk-sensitive planning objectives is
important for building autonomous agents or decision-support systems for
real-world applications. However, this line of research has been largely
ignored in the artificial intelligence and operations research communities
since planning with risk-sensitive planning objectives is more complicated than
planning with risk-neutral planning objectives. To remedy this situation, we
derive conditions that guarantee that the optimal expected utilities of the
total plan-execution reward exist and are finite for fully observable Markov
decision process models with non-linear utility functions. In case of Markov
decision process models with both positive and negative rewards, most of our
results hold for stationary policies only, but we conjecture that they can be
generalized to non stationary policies.
