Optimal Management of the Pension Contribution Rate Using the H∞-Control Theory

In this paper, we construct a general model for a pension fund when there are time delays in the valuation process. Actually, we use the standard structure of the basic reserve equation in order to rebuild a more sophisticated approach based on the theory of H∞ control. Our model evaluates the incomplete information from the delayed fund valuations—due to the oscillatory pattern for benefit claims and investment experience of the past years—within the context of uncertainty additionally to the randomness which certainly exists. So, we construct estimations for the optimal proposed contribution rates based on a feedback mechanism which is a robust stabilization controller, using typical linear matrix inequalities. Finally, a numerical application is fully investigated to obtain further insight into the problem.

Optimal investment for the defined-contribution pension with stochastic salary under a CEV model

In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.

Defined Contribution Pension Planning with the Return of Premiums Clauses and HARA Preference in Stochastic Environments

This paper studies a defined contribution(DC)pension fund investment problem with return of premiums clauses in a stochastic interest rate and stochastic volatility environment.In practice,most of pension plans were subject to the return of premiums clauses to protect the rights of pension members who died before retirement.In the mathematical modeling,we assume that a part of pension members could withdraw their premiums if they died before retirement and surviving members could equally share the difference between accumulated contributions and returned premiums.We suppose that the financial market consists of a risk-free asset,a stock,and a zero-coupon bond.The interest rate is driven by a stochastic affine interest rate model and the stock price follows the Heston’s stochastic volatility model with stochastic interest rates.Different fund managers have different risk preferences,and the hyperbolic absolute risk aversion(HARA)utility function is a general one including a power utility,an exponential utility,and a logarithm utility as special cases.We are concerned with an optimal portfolio to maximize the expected utility of terminal wealth by choosing the HARA utility function in the analysis.By using the principle of dynamic programming and Legendre transform-dual theory,we obtain explicit solutions of optimal strategies.Some special cases are also derived in detail.Finally,a numerical simulation is provided to illustrate our results.

Optimal Investment of Defined Contribution Pension Based on Self-Protection and Minimum Security

This paper mainly studies the optimal investment problem of defined contribution(DC)pension under the self-protection and minimum security.First,we apply Ito?theorem to obtain the differential equation of the real stock price after discounting inflation.Then,under the constraint of external guarantee of DC pension terminal wealth,self-protection is introduced to study the maximization of the expected utility of terminal wealth at retirement time and any time before retirement.The explicit solution of the optimal investment strategy of DC pension at retirement time and any time before retirement should be derived by martingale method.Finally,the influence of selfprotection on the optimal investment strategy of DC pension is numerically analyzed.

Multi-Period Telser's Safety-First Portfolio Selection Problem in a Defined Contribution Pension Plan

This paper investigates a multi-period portfolio optimization problem for a defined contribution pension plan with Telser's safety-first criterion.The plan members aim to maximize the expected terminal wealth subject to a constraint that the probability of the terminal wealth falling below a disaster level is less than a pre-determined number called risk control level.By Tchebycheff inequality,Lagrange multiplier technique,the embedding method and Bellman's principle of optimality,the authors obtain the conditions under which the optimal strategy exists and derive the closed-form optimal strategy and value function.Special cases show that the obtained results in this paper can be reduced to those in the classical mean-variance model.Finally,numerical analysis is provided to analyze the effects of the risk control level,the disaster level and the contribution proportion on the disaster probability and the value function.The numerical analysis indicates that the disaster probability in this paper is less than that in the classical mean-variance model on the premise that the value functions are the same in two models.

CONSTANT ELASTICITY OF VARIANCE MODEL AND ANALYTICAL STRATEGIES FOR ANNUITY CONTRACTS

The constant elasticity of variance（CEV） model was constructed to study a defined contribution pension plan where benefits were paid by annuity. It also presents the process that the Legendre transform and dual theory can be applied to find an optimal investment policy during a participant＇s whole life in the pension plan. Finally, two explicit solutions to exponential utility function in the two different periods （before and after retirement） are revealed. Hence, the optimal investment strategies in the two periods are obtained.

Time-Consistent Investment Strategy for DC Pension Plan with Stochastic Salary Under CEV Model

This paper aims to derive the time-consistent investment strategy for the defined contribution(DC) pension plan under the mean-variance criterion.The financial market consists of a risk-free asset and a risky asset of which price process satisfies the constant elasticity of variance(CEV) model.Compared with the geometric Brownian motion model,the CEV model has the ability of capturing the implied volatility skew and explaining the volatility smile.The authors assume that the contribution to the pension fund is a constant proportion of the pension member's salary.Meanwhile,the salary is stochastic and its volatility arises from the price process of the risky asset,which makes the proposed model different from most of existing researches and more realistic.In the proposed model,the optimization problem can be decomposed into two sub-problems:Before and after retirement cases.By applying a game theoretic framework and solving extended Hamilton-Jacobi-Bellman(HJB) systems,the authors derive the time-consistent strategies and the corresponding value functions explicitly.Finally,numerical simulations are presented to illustrate the effects of model parameters on the time-consistent strategies.