title: Stochastic control problems for pension schemes
Creators: name: Wang, Yongjie
Publisher: name: University of Glasgow
Year: 2022

description: The last decades have witnessed unexpected changes in life expectancy, low financial market returns and surging inflation. Pension schemes all over the world are facing a period of extreme changes and challenges. Risk management in pension schemes is becoming highly complex and tends to be a major economic and financial topic. At the same time, stochastic optimization methods have become important tools used in fields of economics, finance and life insurance. This Ph.D. thesis is devoted to focusing on risk management and asset allocation for pension schemes in a dynamic way. We intend to develop continuous-time stochastic optimization models to tackle pension issues. Chapter 1 overviews pension schemes and risks and briefly discusses the stochastic optimization methods. Chapter 2 studies the longevity risk management in a defined contribution pension scheme that promises a minimum guarantee such that members are able to purchase lifetime annuities upon retirement. To hedge the longevity risk, the scheme manager decides to invest in a mortality-linked security that is available on the financial market, typically a longevity bond. The manager’s compensation depends on the surplus between the scheme’s final wealth and the minimum guarantee. The manager maximizes his expected utility from terminal compensation by controlling the investment strategy. We transform the corresponding constrained optimal investment problem into a single investment portfolio optimization problem by replicating future contributions from members and the minimum guarantee provided by the scheme. We solve the resulting optimization problem using the dynamic programming principle. Through a series of numerical studies, we show that longevity risk has an important impact on investment performance. Our results add to the growing evidence supporting the use of mortality-linked securities for efficient hedging of longevity risk. Chapter 3 investigates the hedging performance of the longevity bond and the role of the risk-sharing rule in a pension scheme. The scheme manager invests in a longevity bond whose coupon payment is linked to a survival index to hedge the longevity risk. We use stochastic affine processes to model the force of mortality and investigate longevity basis risk, which arises when the mortality behavior of the members and the longevity bond’s reference population are not perfectly correlated. The problem is to maximize both member’s and manager’s utilities by controlling the investment strategy and benefit withdrawals. By applying the dynamic programming principle, we derive optimal solutions for the single and sub-population cases. Our numerical results show that the longevity bond acts as an effective hedging instrument, even in the presence of longevity basis risk. Also, we find that the risk-sharing rule is beneficial to both the member and the manager. Chapter 4 turns to the situation where a DB scheme sponsor plans to wind up the scheme via an insurance buy-out. The sponsor’s objective is to minimize the expected quadratic deviation of the terminal scheme wealth from the buy-out cost by deciding the investment strategy and winding up time. We derive the explicit solution to the combined stochastic control and optimal stopping problem by solving the corresponding variational Hamilton-Jacobi-Bellman inequality. Our analyses show that if the scheme wealth is initially lower than the technical provisions, it is optimal to purchase the buy-out when the funding level touches a threshold under specific financial and insurance markets conditions.