Applications of Stochastic Optimization in Finance and Insurance

本提案中概述的研究计划的主要主题是将数学方法从概率和优化应用于保险和金融中不确定条件下的决策问题。该计划旨在有两个方向的发展流，因为数学技术的应用对工业面临的现实世界问题做出了贡献，而新的工业挑战引发了可能导致新的理论发展的数学问题。研究计划主要有三个主题。它们是：1)混合养老金结构及其估值、对冲和管理；2)资产管理收费协议的结构及其创造的激励机制；3)金融机构压力测试数学方法的发展。随着工业养老基金从固定收益安排转向固定缴款安排，混合型养老金结构变得越来越受欢迎。本研究项目所追求的主题将包括计划发起人承诺利益的估值和对冲，计划发起人信誉对养老金福利价值的影响，不同计划结构对员工和计划发起人产生的激励，以及计划管理中的代际公平问题。最近，人们提出了一些新的合同结构，试图克服传统资产管理关系的一些明显缺点。例子包括对冲基金管理协议中的首次损失费结构，以及为参与合同和保险公司提供的可变年金提出的费用。本研究项目将对此类合同的结构进行研究，分析合同结构对双方决策和福利的影响。量化风险管理在全球金融危机之前和期间的失败是众所周知的。传统上，基于历史数据的风险统计度量已经被极端情况下的投资组合损失评估所补充，这个过程通常被称为压力测试。压力场景通常是主观的和特别的，并且已经被满足竞争目标的困难所困扰，这些目标足够极端，以提供对投资组合弹性的真正测试，并且足够合理，以便决策者将认真对待测试结果。本计划的第三个研究课题将是开发用于生成应力情景的定量方法。该研究将解决为内部压力测试目的生成边际情景的问题，以及在给定外部（例如由机构的经济学家或监管机构）指定的经济情景的情况下生成投资组合风险因素条件分布的问题。

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.