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.

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.

The Applicability of the Notional Defined Contribution Model for China

Ⅰ.IntroductionSince 1995,six Asian and European countries(Sweden,Italy,Latvia,Poland,Mongolia andKyrgyz Republic)have introduced variants of an in-novative new defined contribution(DC)security

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.

Financial Feasibility Study of NDC Scheme Based on Comparison of Financial Costs between NDC and FDC Schemes

The establishment of individual accounts is the landmark events for China officially shift from pay-as-you-go pension system to partly funded system. But the process of running personal accounts at the same time also exposed various drawbacks. On the macro level, there is a growing gap between the nominal amount of personal account and the actual accumulated amount, which means the personal account is empty, the personal accounts are being questioned, and the scholars began to seek other solutions. NDC scheme came into being. specific empirical work has been done by using the actuarial model of pension income and expenditure to predict whether NDC is superior to FDC in financial cost by comparing the institutional cost of FDC and NDC from 2015 to 2050. Finally, this paper draws a conclusion that the nominal account system can be used as a choice route for the basic pension system for urban workers in the next 30 years with the assist of relevant supporting measures.

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.

Assessment for Social Security Pilot in Jilin and Hei Longjiang of China

The present paper reviews the social security pilot in Jilin and Hei Longjiang that was carried out between 2004 and 2005. The pilot in the two provinces has basically achieved its main objectives, but there are still some unsolved problems, the most severe being lack of effective investment of the funds accumulated by individual accounts. During periods of high economic growth and high growth in average wages, this problem might undermine the partially-funded security system. To this end, the paper makes some suggestions, one of which is to introduce the notional defined contribution system.