Applications of Stochastic Optimization in Finance and Insurance

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The principal theme of the research program outlined in this proposal is the application of mathematical methods from probability and optimization to problems of decision making under uncertainty in insurance and finance. The program is designed to have development flow in both directions, as applications of mathematical techniques make contributions to real-world problems faced in industry, and novel industrial challenges provoke mathematical questions that may lead to new theoretical developments. Three main topics dominate the research program. These are: i) hybrid pension structures and their valuation, hedging and management, ii) the structure of fee agreements for asset management and the incentives that they create, and iii) the development of the mathematics of stress testing in financial institutions.Hybrid pension structures have become increasingly popular as industrial pension funds have shifted from defined benefit to defined contribution arrangements. Topics pursued in this research program will include the valuation and hedging of the committed benefits of the plan sponsor, the impact of the plan sponsor's creditworthiness on the value of pension benefits, the incentives created by different plan structures for both employees and plan sponsors, and issues of intergenerational fairness within plan management. Recently, a number of novel contract structures have been proposed that have sought to overcome some of the perceived shortcomings of traditional asset management relationships. Examples include first loss fee structures in hedge fund management agreements, and the fees that have been proposed for participating contracts and variable annuities offered by insurers. This research program will pursue the study of the structure of such contracts, analyzing the impact of contract structure on the decisions and welfare of both parties. The failures of quantitative risk management before and during the global financial crisis are well known. Traditionally, statistical measures of risk based on historical data have been supplemented by the evaluation of portfolio losses under extreme scenarios, in a process commonly referred to as stress testing. Stress scenarios have often been subjective and ad hoc, and have been plagued by the difficulties of meeting the competing goals of being sufficiently extreme to provide a true test of portfolio resilience, and plausible enough so that decision makers will take the test results seriously. The third topic of research in this program will be the development of quantitative methods for generating stress scenarios. The research will address the problem of generating marginal scenarios for internal stress testing purposes, and the problem of generating conditional distributions of portfolio risk factors given economic scenarios specified externally, for example by the institution's economists or regulators.