Optimal Investment Strategies And Risk-sharing Arrangements For Hybrid Pension Plans

In the 21 st century,aging of the population is becoming a worldwide problem and the social impact it brings is a common problem faced by all countries in the world today.As the main source of retirement income,pensions play a very important role in redistributing wealth,improving people’s wellbeing,maintaining social stability and promoting social development.However,the aging of population brings about substantial social impact on a country’s macro-economy,finance and society in many aspects.The pension system is facing unprecedented strikes and challenges,and fundamental reformation is urgently required.Getting out of the financial predicament of the pension account and maintaining the balance of payments under the background of population aging will determine the retirement benefits of the people,and even affect the overall social and economic stability.There is no doubt that this produces a daunting task for policymakers.The core goal of pension fund management is to maximize the investment gains while keeping the stability and continuity of the pension system as far as possible.However,whether or not the pension fund’s investment can achieve the target benefits will actually be affected by the financial market and many other economic factors.How to realize the higher endowment insurance for the insured persons through efficient asset allocation is the common goal of scholars and practitioners.In this thesis,pension models are established around the above objectives,and the optimal strategies and the corresponding value functions are derived by using the stochastic dynamic programming method.This thesis is divided into three parts to study the above issues.The first part considers a stochastic model for a target benefit pension plan(TBP)in continuous time.In this model,the plan members’ contributions are set in advance while the benefit outgo depends on the wealth of the pension fund and a specified benefit target.The pension fund is invested in both a risk-free asset and a risky asset.The goal of the plan trustees is to minimize accumulated squared and linear deviations between the benefit outgo and a pre-set target during the whole distribution period as well as to minimize discontinuity risk measured at the end of the period.In particular,stochastic salary rates and the correlation between salary movements and financial market fluctuations are considered.We fix the overall cost of the plan in terms of starting capital and ongoing contribution level and apply stochastic control theory to model the investment and benefit decisions made by the plan sponsors.Using the stochastic optimal control approach,we derive closed-form solutions for optimal investment strategies as well as optimal benefit payment adjustments,which minimize the combination of benefit risk and intergenerational transfers.Finally,numerical analyses are presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market.In the second part,the optimal control problem is studied under the framework of the target benefit pension scheme with loss aversion participants.The plan members are loss averse with an S-shaped utility over benefit relative to a time-varying target benefit level.The objectives of this TBP model is to provide a reasonable retirement benefit(around the pre-set target)to its participants on a sustainable,stable and affordable basis with risk sharing among different age cohorts,while maintaining the financial security of the non-retired participants.Using the martingale method,we derive the optimal investment strategy and the optimal benefit payment policy,explicitly,which minimizes the interim utility of the benefit risk in terms of deviating from the benefit target.It is shown that the target benefit pension plan model for loss-averse participants is effective in providing a stable and sustainable pension account for participants.On the basis of the first two parts,the third part introduces a collective hybrid pension scheme with intergenerational risk sharing in a continuous time framework.The indexation of accrued benefits for active members and the benefit payments for retirees are linked to the fund level of the pension plan.We focus on the strategic portfolio allocation decisions together with pension policies,combining the asset-liability management technique with pension management in a hybrid pension scheme,with both contributions and benefit payments being adjusted based on the pension fund deficiency/surplus to dynamically adjust pension fund’s financial position.In this way risks are shared between different generations.The objective is to seek an optimal investment strategy and optimal risk-sharing arrangements for plan sponsors and participants,which minimize the expected discounted disutility of intermediate adjustment for both benefits and contributions as well as terminal wealth in finite time horizon.Using the stochastic optimal control approach,closed-form solutions are derived under quadratic loss function and exponential loss function,respectively.Numerical analyses are presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market and how the optimal benefit changes with respect to different risk aversions.The aging of population is not only an inevitable trend faced by China,but also has the characteristics of globalization.The above problems are new problems and new directions that pension managers are actually exploring,but they are the first to be studied theoretically.Solving these problems requires the integrated use of financial mathematics and actuarial mathematics.We try to learn from the international pension fund investment experience and analyze the economic significance of the model by combining theory with practice.