Decentralized intensity control and optimal risk transfer

Decentralized decision making is a central issue for resource allocation, revenue management and risk management problems. Instead of assuming the existence of a central agent who has all the information that is needed to make decisions for the entire system, decentralized decision making involves multiple agents with different information sets and control over different parts of the system. Decentralization is often preferred because of its high computational efficiency or flexibility with respect to operational constraints. It is often unavoidable if relevant information is dispersed between multiple agents and can not be collected in a single place for a single decision maker.;The first part of this dissertation concerns decentralized decision making for stochastic control problems. We begin by looking at these issues in the special context of a pricing-service system and then generalize to intensity control problems where revenue is driven by a family of locally Poisson processes over a finite horizon. These results assume risk neutrality for both the centralized and decentralized decision makers. The next part of the dissertation involves risk-averse agents. We introduce the notion of generalized exponential utility and show how the centralized system (with generalized exponential utility) can be decoupled into a family of problems in which individual agents have exponential utility with possibly different risk-aversion levels. We derive two ways of decoupling the central problem, one by taxing and the other by revenue sharing. For each of these, we show the existence of individual problems that deliver the centralized optimal, and design an algorithm that converges to the centralized optimal and preserves information sharing constraints at each iteration.;The second part of the dissertation is in the general area of risk measures, and more specifically, the problem of optimal risk transfer. Optimal risk transfer is the problem of finding a contract that describes the way that cash should be transferred between a group of parties facing correlated risks so as to minimize the total risk for the group. While optimal risk transfer problems are starting to attract research attention, the class of risk measures for which the optimal contract structure can be derived is limited. In the final part of this dissertation, we introduce a new risk measure which we call a generalized entropic risk measure, and apply this measure to risk models defined in terms of jumps as well as Brownian motion. We derive the optimal contract structure associated with this new family of risk measures.