| Since entering the 21st century,with the continuous evolution of the population structure and the rapid development of social economy,the types of insurance funds have become ever more diverse.For pension funds,the phenomenon of population aging has brought unprecedented challenges and strikes to the pension systems,requiring them to seek fundamental reformation.For other insurance funds,realizing the appreciation of insurance funds,improving the solvency of insurers,and considering the joint interests of policyholders and insurers have become the basic demands of insurance policy construction.Thus,in order to make the operation of insurance funds more professional,the decision maker needs to consider various financial market risks,construct the insurance fund model in line with the actual market,and seek a more reasonable investment management method.This thesis stands from the perspective of pension trustees,mainly studies the optimal investment and adjustment problem for target benefit plan,DB pension plan and hybrid pension plan with model uncertainty and different financial market risks.This thesis also stands from the perspective of policyholders and insurers,considers the optimal insurance investment problem with their joint interests under model uncertainty.The thesis firstly studies the optimal investment and payment adjustment problems of the target benefit pension plan(TBP)under model uncertainty and default risk.For this type of pensions,the contributions of participants are predetermined,and the benefits they receive after retirement are determined by the wealth status of the pension account.The terminal wealth and payment of pension have pre-set targets as reference standards.Ambiguity-averse pension trustees invest pension fund into a risk-free asset,a risky asset(stocks)and a defaultable bond to maintain and increase account value.The objective of this pension plan is to maximize the wealth and benefit excess from the target value or minimize the wealth and benefit gap from the target value with exponential function.Applying stochastic control approach,we establish the Hamilton-Jacobi-Bellman equations for both the post-default case and the pre-default case,respectively.Robust optimal investment strategies and benefit payment adjustment strategies are derived explicitly for above two cases.The thesis secondly considers the investment and contribution adjustment strategy for a multi-cohorts DB pension plan in an environment with parameter uncertainty.Since the pension trustees are ambiguous about some risky assets,risky assets in the market are divided into pure risk assets and ambiguous risky assets.Pension trustees invest pension funds in a risk-free asset and two different types of risky assets,use the power-power utility to reflect ambiguity aversion and risk aversion and aim to maximize the expected value of terminal wealth and the accumulated contributions under the smooth ambiguity.This optimization problem is time-inconsistent and cannot be solved by the Bellman Optimality Principle.In order to solve the above time inconsistency problem,the thesis considers the notion of Nash equilibrium,and obtains the equilibrium investment and payment adjustment strategy of a multi-cohorts DB pension plan under smooth ambiguity.Thirdly,the thesis studies the robust optimal investment and pension adjustment strategy with longevity trend for a hybrid pension plan.Different from the TBP and DB pension plans,the contributions and benefits of the hybrid pension scheme are adjusted in continuous time,and the risks of the hybrid pension are shared by the trustees and participants.Ambiguity-averse pension trustees manage their investment by purchasing a risk-free asset and a risky asset in the financial market.Under the exponential loss function,the core goal of pension trustees is to minimize the expectation of the deviation between the actual terminal wealth and the target terminal wealth,and the accumulated pension adjustments.This pension plan aims to find an optimal investment and pension adjustment strategy for pension trustees and participants,which can also reduce the risk of intermediate adjustment for the pension system.Applying the dynamic programming method in the stochastic optimal control theory,we derive the robust optimal investment and pension adjustment strategy and the corresponding value function,respectively.Finally,this thesis considers the joint interests of the policyholder and the insurer in the robust optimal insurance-investment problem,and sets the specific role of the policyholder as the government.With the mispricing phenomenon,information asymmetry exists in the market.As the policyholder,the government purchases a proportional insurance from the insurer for some public infrastructure,and invests in a risk-free asset and a stock whose price process satisfies the geometric Brownian motion in the financial market.The insurer’s surplus process satisfies the classic Cramer-Lundberg(C-L)risk model,and invests in a pair of mispriced stocks,a risk-free asset,and a market index.In addition,the government and the insurer are both ambiguity averse.The goal of them is to maximize the expected joint utility of the government and insurer.By applying stochastic optimal control approach,we obtain the explicit expressions of the robust optimal insurance-investment strategy.By establishing the mathematical models for the optimal investment management problem of insurance funds,this thesis studies the impact of market risks and model uncertainty on optimal strategies,and provides a certain reference for the management of insurance funds,especially for pension funds.In addition,in order to visually display the model results,numerical simulations are given at the end of each investigation to analyze the sensitivity of the optimal strategy to the model parameters. |
