Final Report Summary - RISK (Risk-Sensitive Policy Making for Populations) The project RISK aims at producing a unified theory of risk-sensitive policy making for populations with applications to various individual, medical, and governmental decision-making situations. The project relies on the use of mathematical tools from operations research, statistics, and economics to formulate risk-sensitive policy making problems involving populations, to obtain efficient computational solution techniques, to generate insights into the effects of varying risk posture and fully or partially resolving uncertainty. Mathematical formulation of dynamic population decision problems is an important step toward systematizing policy making and eliminating arbitrariness in this process. In doing this, the choice of performance criteria against which to benchmark available alternatives is essential. Equally important is the determination of the relationships between individuals involved in the model, i.e. whether they compete against each other or cooperate, whether their actions are correlated in any way or not. Interactions between individuals determine the nature of the problem, the solution methodologies, and the complexity. Accordingly, theoretical models considered in the project are classified as optimization models, where a central authority determines an optimal policy for the entire population, and game-theoretic models, where individuals pursue their own objectives when faced with different decision alternatives. RISK is intended to elicit the impact of adopting various probabilistic criteria like mean, expected utility, and mean-variance criteria, for both types of models. The objectives of RISK are defined as:- Objective 1: To develop a unified theory of risk management for populations,- Objective 2: To apply the resulting theory to public policy making.While these two objectives are intertwined, the first period of the project focused on Objective 1 while the second one was devoted to Objective 2. In the first period, existing population models were reviewed and their appropriateness for various population types was evaluated. Optimization models under optimality criteria including expected return, risk-averse utility, and extinction probability were developed for multi-type branching processes. The existence and the characterization of optimal policies were explored. Risk-sensitive criteria were also investigated in several game-theoretic models that arise in the formulation of certain societal problems. For the models investigated, the policies obtained from optimization and game-theoretic models were compared. The three categories of mathematical models identified in this period were controlled multi-type branching processes (or Markov population decision chains), stochastic contests, and queuing systems, under risk-sensitive decision criteria. The second period of the project involved the implementation of the results obtained in the first period to various arenas concerning social welfare. To this end, several applications for each stochastic model considered in the first period were proposed, and the results were illustrated through numerical experiments. These applications involve the analysis and design of public service systems like healthcare and transportation systems, the management of epidemic diseases, the assessment of medical treatment alternatives, the regulations to prevent the extinction of endangered species, the regulations concerning the use of natural resources, and the choice of countermeasures against natural and planned disasters. More specifically, some ecological and medical applications were studied by using the theory on Markov population decision chains. The theory on stochastic contests was applied to the allocation of available resources to reduce (or to eliminate if possible) potential losses from natural disasters and planned attacks, and the results of investigated queuing models were interpreted within the context of public services including the analysis and design of public transport systems, and the governmental regulations concerning healthcare services. In each case, the main study purposes were to understand the effects of fully or partially eliminating uncertainty, to carry out the analysis under varying risk-sensitive criteria, and to identify the values of the system design parameters maximizing social welfare.Overall, the project contributes to the theory of analysis and optimization of stochastic systems, and paves the way for a novel practice of evaluating current policies and proposing rather robust policies when necessary. The adoption of such an approach in decision making, in particular in governmental contexts, has the potential to reinforce the soundness of decisions concerning the public and consequently improve the social welfare.The researcher greatly benefited from the Marie Curie Career Integration Grant, which funded this project, and the opportunities offered by Koc University. Thanks to these, the researcher could independently pursue her research interests, teach courses aligned with these interests, explore new research directions, and initiate productive and hopefully long-lasting collaborations. The researcher hopes that the outcomes of this research will be useful also for the society by affecting the public-policy making practice. The web site of RISK is located at http://home.ku.edu.tr/~pcanbolat/risk.html.
