Pension funding with moving average rates of return. (English) Zbl 0971.91040
A stationary benefit plan is considered with random rates of returns on assets \(R_t\) for stationary population. It is supposed that \(R_t\) is a moving average sequence of any order. Using a technique of Markovian representation for bilinear processes the authors derive explicit expressions for the means and variances of the fund level and the actuarial loss. In the numerical examples considered by the authors is \(R_t=r+e_t+de_{t-1}\), where \(e_t\) are i.i.d. with Beta(2,2) distribution.
Reviewer: R.E.Maiboroda (Kyïv)
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 60J05 | Discrete-time Markov processes on general state spaces |
References:
| [1] | Bédard D., Modélisation stochastique des caisses de retraite (1997) |
| [2] | Cairns A. J. G., Insurance: Mathematics and Economies 21 pp 43– (1997) |
| [3] | Conlisk J., Int. Econ. Rev. 15 pp 523– (1974) · Zbl 0283.60065 · doi:10.2307/2525877 |
| [4] | Dufresne D., The dynamics of pension funding (1986) · Zbl 0606.62123 |
| [5] | Dufresne D., Insurance and risk theory pp 277– (1986) · doi:10.1007/978-94-009-4620-0_18 |
| [6] | Dufresne D., Journal of the Institute of Actuaries 115 pp 535– (1988) · doi:10.1017/S0020268100042815 |
| [7] | Dufresne D., Insurance: Mathematics and Economics 8 pp 71– (1989) · Zbl 0704.62096 |
| [8] | Dufresne D., Actuarial Research Clearing House pp 111– (1990) |
| [9] | Dufresne D., Transactions of the Twenty-Fourth International Actuarial Congress, Montreal 1 pp 27– (1992) |
| [10] | Dufresne D., Actuarial Research Clearing House 2 pp 1– (1993) |
| [11] | Dufresne D., Mathématiques des caisses de retraite (1994) |
| [12] | Gerrard R. J., Insurance: Mathematics and Economics 18 pp 59– (1996) |
| [13] | Granger C. W., An introduction to bilinear time series model (1978) · Zbl 0379.62074 |
| [14] | Guégan D., J. Time Ser. Anal. 8 pp 389– (1987) · Zbl 0653.62065 · doi:10.1111/j.1467-9892.1987.tb00003.x |
| [15] | Haberman S., ARCH pp 141– (1990) |
| [16] | Haberman, S. Stochastic approach to pension funding methods. Proceedings of the first AFIR colloquium. 1990, Paris. Volume 4, pp.93–112. |
| [17] | Haberman, S. Pension funding methods and autoregressive interest rate models. Proceedings ofthe 2nd AFIR colloquium. 1991, Brighton. Volume 2, pp.181–204. |
| [18] | Haberman, S. Pension funding methods and autoregressive interest rate models. Proceedings of the 24th international actuarial congress. 1992, Montréal. Vol. 4, pp.83–98. |
| [19] | Haberman S., Insurance: Mathematics and Economics 13 pp 45– (1993) |
| [20] | Haberman S., Insurance:Mathematics and Economics 13 pp 263– (1993) |
| [21] | Haberman S., Insurance: Mathematics and Economics 14 pp 219– (1994) |
| [22] | Haberman S., Insurance: Mathematics andEconomics 20 pp 115– (1997) |
| [23] | Pham D., Stochastic Processes and theirApplications 20 pp 295– (1985) · Zbl 0588.62162 · doi:10.1016/0304-4149(85)90216-9 |
| [24] | Pham D. T., Stochastic Processes and their Applications 23 pp 291– (1986) · Zbl 0614.60062 · doi:10.1016/0304-4149(86)90042-6 |
| [25] | Nicholls D. F., Random coefficient autoregressive models: an introduction. LectureNotes in Statistics 11 (1982) · Zbl 0497.62081 · doi:10.1007/978-1-4684-6273-9 |
| [26] | Zimbidis A., Insurance: Mathematics and Economics 13 pp 271– (1993) |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
