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 Market Reaction to the Pronouncements Related to International Accounting Standards （IAS） 19R

This paper examines whether and how investors reacted to the pronouncements related to International Accounting Standards （IAS） 19R. Using a sample of 401 European firms reporting pension and retirement expense during the period of 2006-2011, this paper finds negative abnormal returns around the pension project initiation by the International Accounting Standards Board （IASB）. More importantly, the abnormal returns are more negative for firms with higher financial leverage and lower ratios of net periodic pension cost to net income, but less negative for firms in countries with weak creditor rights （CR） and infrequent use of the corridor approach under IAS 19. Additionally, the effects of financial leverage and the ratio of net periodic pension cost to net income on the abnormal returns are more pronounced for smaller firms. Overall, the results are consistent with the view that recognition of previously disclosed off-balance-sheet pension liabilities as required by IAS 19R increases debt contracting costs, and highlight the importance of considering firm size and CR in international tests of debt contracting theory.

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.

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.

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.

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.

Optimal Investment Strategy of Target Benefit Pension Plan Based on Random Inflation and Intergenerational Risk

In this paper,based on the stochastic optimal control method,the intergenerational risk and inflation risk,the optimal investment strategy of the target benefit pension plan is investigated on the basis of measuring the random wage rate under the random mortality and inflation risk of the personnel in the plan and the correlation between the wage change and the fluctuation of the financial market.The research shows that the financial market parameters and wage rate have a great influence on the optimal investment strategy,and gives the optimal investment strategy and the optimal income adjustment strategy of the target benefit pension.The research of this paper provides a reference for the policy formulation and implementation of the Target Benefit Pension Plan in our country.

Optimal portfolio for a defined-contribution pension plan under a constant elasticity of variance model with exponential utility

Based on the Lie symmetry method,we derive the explicit optimal invest strategy for an investor who seeks to maximize the expected exponential(CARA)utility of the terminal wealth in a defined-contribution pension plan under a constant elasticity of variance model.We examine the point symmetries of the Hamilton-Jacobi-Bellman(HJB)equation associated with the portfolio optimization problem.The symmetries compatible with the terminal condition enable us to transform the(2+1)-dimensional HJB equation into a(1+1)-dimensional nonlinear equation which is linearized by its infinite-parameter Lie group of point transformations.Finally,the ansatz technique based on variables separation is applied to solve the linear equation and the optimal strategy is obtained.The algorithmic procedure of the Lie symmetry analysis method adopted here is quite general compared with conjectures used in the literature.