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Pension funding incorporating downside risks. (English) Zbl 1074.91547

Summary: This research extends S. Haberman and J.-H. Sung’s [Insur. Math. Econ. 15, 151–162 (1994; Zbl 0818.62091)] and Chang’s [ibid. 24, 187–199 (1999; Zbl 0959.91024)] 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
91B28 Finance etc. (MSC2000)
93C95 Application models in control theory
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[1] Bacinello, A.R., A stochastic simulation procedure for pension scheme, Insurance: mathematics and economics, 7, 153-161, (1988) · Zbl 0667.62073
[2] Benjamin, S., 1984. An actuarial layman looks at control theory. In: Proceedings of the Transactions of 22nd International Congress of Actuaries, pp. 295-310.
[3] Benjamin, S., Driving the pension fund, Journal of institute of actuaries, 116, 717-735, (1989)
[4] Bowers, N.L.; Gerber, H.U.; Hickman, J.C.; Jones, D.A.; Nesbitt, C.J., Notes on the dynamics of pension funding, Insurance: mathematics and economics, 1, 261-270, (1982) · Zbl 0526.62095
[5] Cairns, A.J.; Parker, G., Stochastic pension fund modeling, Insurance: mathematics and economics, 21, 43-79, (1997) · Zbl 0919.62118
[6] Chang, S.C., Optimal pension funding through dynamic simulations: the case of Taiwan public employees retirement system, Insurance: mathematics and economics, 24, 187-199, (1999) · Zbl 0959.91024
[7] Chang, S.C., Realistic pension funding: a stochastic approach, Journal of actuarial practice, 8, 5-42, (2000) · Zbl 1066.91056
[8] Chang, S.C.; Chen, C.C., Allocating unfunded liability in pension valuation under uncertainty, Insurance: mathematics and economics, 30, 371-387, (2002) · Zbl 1074.62525
[9] Chang, S.C.; Cheng, H.Y., Pension valuation under uncertainties: implementation of a stochastic and dynamic monitoring system, Journal of risk and insurance, 69, 171-192, (2002)
[10] Cox, J.C.; Ingersoll, J.E.; Ross, S.A., An intertemporal general equilibrium model of asset prices, Econometrica, 53, 2, 363-384, (1985) · Zbl 0576.90006
[11] Daykin, C.D., Pentikainen, T., Pesonen, M., 1994. Practical Risk Theory for Actuaries, Monographs on Statistics and Applied Probability, vol. 53. Chapman & Hall, London, UK. · Zbl 1140.62345
[12] Dufresne, D., Moments of pension fund contributions and fund levels when rates of return are random, Journal of the institute of actuaries, 115, 535-544, (1988)
[13] Dufresne, D., Stability of pension systems when rates of return are random, Insurance: mathematics and economics, 6, 129-134, (1989) · Zbl 0666.62105
[14] Gerrard, R.J.; Haberman, S., Stability of pension systems when gains/losses are amortized and rates of return are autoregressive, Insurance: mathematics and economics, 18, 59-71, (1996) · Zbl 0914.62089
[15] Haberman, S., Pension funding with time delays: a stochastic approach, Insurance: mathematics and economics, 11, 179-189, (1992) · Zbl 0764.62090
[16] Haberman, S., Pension funding with time delays and autoregressive rates of investment return, Insurance: mathematics and economics, 13, 45-56, (1993) · Zbl 0789.62087
[17] Haberman, S., Autoregressive rates of return and the variability of pension contributions and fund levels for a defined benefit pension scheme, Insurance: mathematics and economics, 14, 219-240, (1994) · Zbl 0808.62097
[18] Haberman, S.; Sung, J.H., Dynamic approaches to pension funding, Insurance: mathematics and economics, 15, 151-162, (1994) · Zbl 0818.62091
[19] Haberman, S.; Wong, L.Y., Moving average rates of return and the variability of pension contributions and fund levels for a defined benefit pension scheme, Insurance: mathematics and economics, 20, 115-135, (1997) · Zbl 0906.62111
[20] Mandl, P.; Mazurova, L., Harmonic analysis of pension funding methods, Insurance: mathematics and economics, 17, 203-214, (1996) · Zbl 0853.62083
[21] McKenna, F.W., Pension plan cost risk, Journal of risk and insurance, 49, 193-217, (1982)
[22] O’Brian, T., A stochastic-dynamic approach to pension funding, Insurance: mathematics and economics, 5, 141-146, (1986) · Zbl 0587.62191
[23] O’Brian, T., A two-parameter family of pension contribution functions and stochastic optimization, Insurance: mathematics and economics, 6, 129-134, (1987)
[24] Owadally, M.I.; Haberman, S., Pension fund dynamics and gain/losses due to random rates of investment return, North American actuarial journal, 3, 105-117, (1999) · Zbl 1082.62543
[25] Owadally, M.I., Haberman, S., 2000. Efficient Amortization of Actuarial Gains/Losses and Optimal Funding in Pension Plans. Actuarial Research Paper No. 133. Department of Actuarial Science and Statistics, City University, London.
[26] Vanderbroek, M., Pension funding and optimal control, Mitteilungen der schweizerische vereinigung der versicherungamathematiker, 2, 313-325, (1990)
[27] Yeh, S.K.; Lin, B.H., Empirical investigation on the Taiwan term structure of interest rates models: an application of the state space model, Review of securities and futures markets, 10, 55-88, (1998)
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.