Pension funding incorporating downside risks

Abstract This research extends Haberman and Sung’s [Insurance: Mathematics and Economics 15 (1994) 151] and Chang’s [Insurance: Mathematics and Economics 24 (1999) 187] works to study optimal funding strategies through the control mechanism. The paper further generalizes the previous research in three ways. First, downside risks, under-funding risk and over-contributing risk, are included additionally in the risk minimization criterion to obtain the optimal solutions. Second, we allow the weighting factors in the performance criterion to belong to a broader parametric family. Third, the rates of investment returns are assumed to follow the auto-regressive process. The above three generalization indeed include traditional model as special cases. Furthermore, an actual case is employed to investigate their financial impacts on funding and contribution due to our generalization. The results show that neglecting to recognize the under-funding risk and the over-contribution risk will lead to a significant difference in optimal funding schedule. The weighting factors and the returns of investment also play critical roles in obtaining the optimal strategy.

[1]  J. C. Hickman,et al.  Notes on the dynamics of pension funding , 1982 .

[2]  S. Haberman.  Pension funding with time delays and autoregressive rates of investment return , 1993 .

[3]  D. Dufresne.  Movements of pension contributions and fund levels when rates of return are random , 1988 .

[4]  Anna Rita Racinello.  A stochastic simulation procedure for pension schemes , 1988 .

[5]  Shih‐Chieh Chang,et al.  Allocating unfunded liability in pension valuation under uncertainty , 2002 .

[6]  R. Gerrard,et al.  Stability of pension systems when gains/losses are amortized and rates of return are autoregressive , 1996 .

[7]  S. Haberman.  Pension funding with time delays: A stochastic approach , 1992 .

[8]  Shih‐Chieh Chang.  Realistic Pension Funding: A Stochastic Approach , 2000 .

[9]  Lam Yuk Wong,et al.  Moving average rates of return and the variability of pension contributions and fund levels for a defined benefit pension scheme , 1997 .

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

[11]  S. Haberman.  Autoregressive rates of return and the variability of pension contributions and fund levels for a defined benefit pension scheme , 1994 .

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

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

[14]  Practical Risk Theory for Actuaries , 1993 .

[15]  D. Dufresne.  Stability of pension systems when rates of return are random , 1989 .

[16]  P. Mandl,et al.  Harmonic analysis of pension funding methods , 1996 .

[17]  S. Haberman,et al.  Efficient amortization of Actuarial gains/losses and optimal funding in pension plans , 2000 .

[18]  Shih‐Chieh Chang,et al.  Pension Valuation Under Uncertainties: Implementation of a Stochastic and Dynamic Monitoring System , 2002 .

[19]  S. Ross,et al.  AN INTERTEMPORAL GENERAL EQUILIBRIUM MODEL OF ASSET PRICES , 1985 .

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

[21]  G. Parker,et al.  Stochastic pension fund modelling , 1997 .

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

[23]  Fred Mckenna.  Pension Plan Cost Risk , 1982 .