Funding and investment decisions in a stochastic defined benefit pension plan with several levels of labor-income earnings

In this paper we consider the optimal management of an aggregated dynamic pension fund. There are n classes of workers whose salaries are stochastic. A portion of the salary is contributed to the funding process and the manager invests in a portfolio with m risky assets and a risk-free security. The main objective is to minimize the cost of contributions in a bounded horizon T and to maximize the utility of final surplus, measured as the relative fund level respect to the mean salary. The aim of the paper is to describe the properties of fund allocation and optimal contribution when salaries differ across contributors to the fund.

[1]  R. C. Merton,et al.  Optimum consumption and portfolio rules in a continuous - time model Journal of Economic Theory 3 , 1971 .

[2]  R. C. Merton,et al.  Optimum Consumption and Portfolio Rules in a Continuous-Time Model* , 1975 .

[3]  W. Fleming,et al.  Hedging in incomplete markets with HARA utility , 1997 .

[4]  D. Duffie,et al.  Optimal Investment With Undiversifiable Income Risk , 1993 .

[5]  Guy Laroque,et al.  Asset Pricing and Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption Goods , 1987 .

[6]  David Blake,et al.  Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans , 2006 .

[7]  J. C. Hickman,et al.  THE DYNAMICS OF PENSION FUNDING: CONTRIBUTION THEORY , 1978 .

[8]  M. I. Owadally.  Pension Fund Dynamics and Gains/Losses Due to Random Rates of Investment Return , 1999 .

[9]  Steven Haberman,et al.  Optimal investment strategies and risk measures in defined contribution pension schemes , 2002 .

[10]  Jean Boulier,et al.  Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund , 2001 .

[11]  S. Haberman.  Pension funding: The effect of changing the frequency of valuations , 1993 .

[12]  G. Deelstra,et al.  Optimal investment strategies in the presence of a minimum guarantee , 2003 .

[13]  Andrew J. G. Cairns,et al.  Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time , 2000, ASTIN Bulletin.

[14]  Arjan Berkelaar,et al.  Retirement Saving with Contribution Payments and Labor Income as a Benchmark for Investments , 2003 .

[15]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[16]  Ricardo Josa-Fombellida,et al.  Optimal risk management in defined benefit stochastic pension funds , 2004 .

[17]  S. Haberman.  Stochastic investment returns and contribution rate risk in a defined benefit pension scheme , 1997 .

[18]  Steven Haberman,et al.  Contribution and solvency risk in a defined benefit pension scheme , 2000 .

[19]  R. C. Merton,et al.  Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case , 1969 .

[20]  Greg Taylor,et al.  Stochastic control of funding systems , 2002 .

[21]  Paolo Battocchio,et al.  Optimal pension management in a stochastic framework , 2004 .

[22]  Steven Haberman,et al.  Optimal investment strategy for defined contribution pension schemes , 2001 .

[23]  D. Duffie.  Dynamic Asset Pricing Theory , 1992 .

[24]  T. Zariphopoulou.  Consumption-Investment Models with Constraints , 1994 .

[25]  Optimal Portfolio Strategies with Stochastic Wage Income and Inflation: The Case of a Defined Contribution Pension Plan , 2002 .

[26]  Thomas J. O'Brien.  A stochastic-dynamic approach to pension funding , 1986 .

[27]  S. Shreve,et al.  Methods of Mathematical Finance , 2010 .

[28]  G. Deelstra,et al.  Optimal investment strategies in a CIR framework , 2000, Journal of Applied Probability.

[29]  Ricardo Josa-Fombellida,et al.  Minimization of risks in pension funding by means of contributions and portfolio selection , 2001 .

[30]  Hyeng Keun Koo,et al.  Consumption and Portfolio Selection with Labor Income: A Continuous Time Approach , 1998 .

[31]  Thomas J. O'Brien.  A two-parameter family of pension contribution functions and stochastic optimization☆ , 1987 .

[32]  Steven Haberman,et al.  Dynamic approaches to pension funding , 1994 .

[33]  D. Williams.  STOCHASTIC DIFFERENTIAL EQUATIONS: THEORY AND APPLICATIONS , 1976 .

[34]  Larry Y. Tzeng,et al.  Pension funding incorporating downside risks , 2003 .

[35]  Shih-Chieh Chang,et al.  Optimal pension funding through dynamic simulations: the case of Taiwan public employees retirement system , 1999 .