×

Optimal contributions in a defined benefit pension scheme with stochastic new entrants. (English) Zbl 1117.91380

Summary: This paper focuses on the impact of the stochastic evolution of the active membership population on the mismatch between assets and liabilities of a defined benefit pension scheme. Classical results in the actuarial literature on pension plan population theory have been extended to the stochastic case. The paper formulates the trade-off between risk and cost of contribution strategies. Then, using a constrained nonlinear programming approach, optimal contributions strategies have been derived and the trade-off solved by means of identifying an efficient frontier. Finally, a numerical application has been carried out, showing the inefficiency of certain classical normal cost methods.

MSC:

91B30 Risk theory, insurance (MSC2010)
91D20 Mathematical geography and demography
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Aitken, W.H., A problem solving approach to pension funding and valuation, (1996), ACTEX Publications Winsted, CT
[2] Artzner, P.; Delbaen, F.; Eber, J.-M.; Heath, D., Coherent measures of risk, Math. finance, 9, 3, 203-228, (1999) · Zbl 0980.91042
[3] Bowers, N.L.; Hickman, J.C.; Nesbitt, C.J., Introduction to the dynamics of pension funding, Trans. soc. actuaries, 28, 177-203, (1976)
[4] Chang, S.C.; Tsai, C.H.; Tien, C.J.; Tu, C.Y., Dynamic funding and investment strategy for defined benefit pension schemes: a model incorporating asset-liability matching criteria, J. actuarial pract., 10, 1, (2002) · Zbl 1062.91044
[5] Chiang, A.C., Fundamental methods in economics, (1984), McGraw-Hill
[6] Dufresne, D., Moments of pension contributions and fund levels when rates of return are random, J. inst. actuaries, 115, 535-544, (1988)
[7] Exley, C.J.; Mehta, S.J.B.; Smith, A.D., The financial theory of defined benefit pension schemes, Br. actuarial J., 3, 835-966, (1997)
[8] Guo, L.; Huang, Z., A possibilistic linear programming method for asset allocation, J. actuarial pract., 4, 1, 67, (1996) · Zbl 1063.91515
[9] Haberman, S.; Sung, J.H., Dynamic approaches to pension funding, Insur.: math. econ., 15, 151-162, (1994) · Zbl 0818.62091
[10] Janssen, J.; Manca, R., A realistic non-homogeneous stochastic pension funds model on scenario basis, Scand. actuarial J., (1997) · Zbl 1078.62531
[11] Josa-Fombellida, R.; Rincón-Zapatero, J.P., Optimal risk management in defined benefit stochastic pension funds, Insur.: math. econ., 34, 489-503, (2004) · Zbl 1188.91202
[12] Keyfitz, N., Applied mathematical demography, (1985), Springer-Verlag · Zbl 0597.92018
[13] Kuhn, H.W.; Tucker, A.W., Nonlinear programming, (), 481-492 · Zbl 0044.05903
[14] Lee, E.M., Introduction to pension schemes, Inst. actuaries, (1986)
[15] Mandl, P.; Mazurova, L., Harmonic analysis of pension funding methods, Insur.: math. econ., 17, 203-214, (1996) · Zbl 0853.62083
[16] Owadally, M.I., 1998. The dynamics and control of pension funding. PhD Thesis. School of Mathematics, The City University, London, UK.
[17] Owadally, M.I., Pension funding and the actuarial assumption concerning investment returns, ASTIN bull., 33, 2, 289-312, (2003) · Zbl 1098.91058
[18] Owadally, M.I.; Haberman, S., Pension fund dynamics and gains/losses due to random rates of investment return, North am. actuarial J., 3, 3, 105, (1999) · Zbl 1082.62543
[19] Owadally, M.I.; Haberman, S., Efficient gain and loss amortization and optimal funding in pension plans, N. am. actuarial J., 8, 1, 21-36, (2004) · Zbl 1085.62509
[20] Owadally, M.I.; Haberman, S., The treatment of assets in pension funding, ASTIN bull., 34, 2, 425-433, (2004) · Zbl 1159.91407
[21] Pitacco, E., Survival models in a dynamic context: a survey, Insur.: math. econ., 35, 2, 279-298, (2004) · Zbl 1079.91050
[22] Rockafellar, R.T.; Uryasev, S., Optimization of conditional value-at-risk, J. risk, 2, 3, 21-41, (2000)
[23] Rustem, B., Algorithms for nonlinear programming and multiple objective decisions, (1998), John Wiley and Sons Ltd. · Zbl 0905.90164
[24] Sharp, K.P., Pension funding by normal costs or amortization of unfunded liabilities, J. actuarial pract., 4, 1, 257-274, (1996) · Zbl 1061.91504
[25] Trowbridge, C.L., Fundamentals of pension funding, Trans. soc. actuaries, 4, 17-43, (1952), 657-683
[26] Winklevoss, H.E., Pension mathematics with numerical illustrations, (1993), University of Pennsylvania Press
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.