Research On Optimal Investment Strategies For DC Pension Plans Based On Ambiguity Aversion And Partial Information

As the most important component of the society security system,pension funds provide the major income source for retirees to maintain their standard of living.S-ince the maintenance and appreciation of pension funds is closely related to people's life and social stability,it is very important to manage the investment of pension funds effectively.In recent years,with the growing aging population and declining fertility rate,the optimal investment decisions for pension plans gradually become the focus of attention in academia and industry.However,the previous literature on the optimal investment of DC pension plans assumes that the decision makers are ratio-nal and computationally unconstrained.Obviously,this assumption is difficult to be satisfied in the real world,and decision makers often cannot accurately know the true probability measure and related parameters of the financial model.The former means that any particular probability measure used to describe a financial model would be subject to a large degree of uncertainty,that is,such uncertainty cannot be represent-ed by a single probability measure,which is called ambiguity(model uncertainty).In this case,decision makers want to seek a robust optimal investment decision to deal with the possible worst-case scenarios caused by the derivation of the estimated prob-ability measure from the true probability measure.The latter implies that decision makers can only estimate unknown parameters based on existing information and new information obtained in the future,which is called partial information(incomplete in-formation).At present,ambiguity and partial information have become the research focus in the field of mathematical finance and insurance actuarial.Therefore,based on literature,through theoretical approach(stochastic dynamic programming,robust optimal control,optimal filtering techniques,derivatives pricing theory and so on),we first investigate the impact of ambiguity on the optimal asset allocation of DC pension plans in the inflation risk and mean-reverting risk premium,as well as the stochastic interest rate and stochastic volatility framework,respectively.Subsequent-ly,we derive the optimal time-consistent investment strategy for DC pension plans under partial information and stochastic interest rate.Finally,we consider the role of the learning effects with return predictability in the optimal investment strategy of DC pension plans.All the specific optimization problems are given as follows.First,we investigate a robust optimal portfolio choice problem for an ambiguity-averse member(AAM)of a defined contribution(DC)pension plan.The AAM has a stochastic salary,considers inflation risk,and invests his/her pension account wealth into a financial market consisting of a risk-free asset,an inflation-indexed bond and a stock whose expected return rate follows a mean-reverting process.His/Her aim is to maximize the expected power utility from his/her terminal real wealth under the worst-case scenario.By using the stochastic dynamic programming approach,the robust optimal investment strategy and the corresponding value function are explicitly derived,and subsequently a verification theorem is provided.Furthermore,two special cases of our portfolio model are discussed.Finally,a numerical example is presented to reveal economic implications of our theoretical results and to illustrate the effects of the model parameters on the robust optimal investment strategy.We find that ambiguity about the dynamics of the inflation-indexed bond price and the stock price and expected return has different influences on the robust optimal investment strategy,and that neglecting ambiguity will always lead to utility loss for the A AM.Second,we formulate a robust optimal investment problem for an ambiguity-averse member(AAM)of defined contribution(DC)pension plans with stochastic interest rate and stochastic volatility.The AAM has access to a risk-free asset,a bond and a stock in a financial market.We assume that the interest rate is described by an affine model,which includes the Cox-Ingersoll-Ross model and the Vasicek model as special cases,while the stock price is driven by the Heston's stochastic volatility model.Moreover,the AAM has different levels of ambiguity aversion about the diffusion parts of the interest rate and the stock's price and volatility.He/She attempts to maximize the expected power utility of his/her terminal wealth under the worst-case scenario.By applying the stochastic dynamic programming approach,we derive a robust optimal investment strategy and the corresponding value function explicitly,and subsequently two special cases are discussed.Finally,a numerical example is presented to illustrate the impact of model parameters on the robust optimal investment strategy and to explain the economic meaning of our theoretical results.The numerical example shows that the AAM's ambiguity aversion levels about the interest rate and the stock's price and volatility have different impacts on the proportions invested in the risky assets,and that ignoring ambiguity always incurs utility losses for the AAM.Third,we discuss an optimal investment problem under partial information and mean-variance criterion for a defined-contribution(DC)pension plan member within a game theoretic framework.We assume that the instantaneous interest rate follows the Vasicek interest model,while the expected return of the stock cannot be com-pletely observed by the member,namely the market price of the stock market risk is described by an unobservable mean-reverting process.The member aims to maximize the mean-variance utility from the terminal wealth exceeding the minimum guaran-tee by investing his/her pension account wealth in a financial market consisting of a cash,a stock and a bond.To solve the partially observable optimization prob-lem,we first transform it to a completely observable investment problem by using the filtering theory.Subsequently,we transform the obtained completely observable investment problem to a self-financing investment problem.Then,by solving the extend Hamilton-Jacobi-Bellman(HJB),we derive the closed-form time-consistent investment strategy and the corresponding value function.Furthermore,we compare results under partial information with the optimal investment strategy when the stock return is completely observable.Finally,some numerical illustrations and sensitivity analysis are presented.Finally,we consider an optimal investment problem for a DC pension plan mem-ber under learning.The expected excess return of the stock is predictable by an observable predictor and an unobservable predictor,and the member has to use op-timal filtering techniques to learn about the latter.Moreover,inflation risk and salary risk are also considered in our model.By using the stochastic dynamic pro-gramming method,we obtain closed-form solutions for the optimal strategy and the corresponding value function.We find that stock return predictability and the correla-tion between the stock and the inflation-indexed bond significantly affect the optimal inflation-indexed bond portfolio.In addition,using the inflation-indexed bond to learn about or hedge against the stock predictors may lead to considerable welfare improvements.