×

A stochastic programming model for funding single premium deferred annuities. (English) Zbl 0874.90149

Summary: Single Premium Deferred Annuities (SPDAS) are investment vehicles, offered to investors by insurance companies as a means of providing income past their retirement age. They are mirror images of insurance policies. However, the propensity of individuals to shift part, or all, of their investment into different annuities creates substantial uncertainties for the insurance company. In this paper we develop a multiperiod, dynamic stochastic program that deals with the problem of funding SPDA liabilities. The model recognizes explicitly the uncertainties inherent in this problem due to both interest rate volatility and the behavior of individual investors. Empirical results are presented with the use of the model for the funding of an SPDA liability stream using government bonds, mortgage-backed securities and derivative products.

MSC:

90C15 Stochastic programming
90C90 Applications of mathematical programming

Software:

MSLiP
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] M.R. Asay, P.J. Bouyoucos and A.M. Maroiano, ”An economic approach to valuation of single premium deferred annuities,” in: S.A. Zenios, ed.Financial Optimization (Cambridge University Press, Cambridge, 1993) pp. 101–135.
[2] D.F. Babbel and S.A. Zenios, ”Pitfalls in the analysis of option-adjusted spreads,”Financial Analysis Journal, July/August (1992) 65–69.
[3] F. Black, E. Derman and W. Toy, ”A one-factor model of interest rates and its application to treasury bond options,”Financial Analysts Journal, January/February (1990) 33–39.
[4] S.P. Bradley and D.B. Crane, ”A dynamic model for bond portfolio management,”Management Science 19(2) (1972) 139–151.
[5] H. Dahl, A. Meeraus and S.A. Zenios, ”Some financial optimization models: I, Risk management,” in: S.A. Zenios, ed.,Financial Optimization Cambridge University Press, Cambridge, 1993) pp. 3–36.
[6] F.J. Fabozzi and I.M. Pollack, eds.,The Handbook of Fixed Income Securities (Dow-Jones, Irwin, Homewood, IL, 1987).
[7] H.I. Gassmann, ”MSLiP: A computer code for the multistage stochastic linear programming problem,”Mathematical Programming 47 (1990) 407–423. · Zbl 0701.90070
[8] B. Golub, M. Holmer, R. McKendall, L. Pohlman and S.A. Zenios, ”A stochastic programming model for money management,”European Journal of Operational Research 85 (2) (1995) 282–296. · Zbl 0912.90020
[9] R.R. Grauer and N.H. Hakansson, ”Higher retum, lower risk: Historical returns on long run, actively managed portfolios of stocks, bonds and bills,”Financial Analysts Journal, March/April (1982) 1936–1978.
[10] R.R. Grauer and N.H. Hakansson, ”Returns on levered actively managed long-run portfolios of stocks, bonds and bills,”Financial Analysts Journal, September (1985) 24–43.
[11] R.S. Hiller and J. Eckstein, ”Stochastic dedication: Designing fixed income portfolios using massively parallel Benders decomposition,”Management Science 39(11) (1994) 1422–1438. · Zbl 0800.90064
[12] R.S. Hiller and C. Schaack, ”A classification of structured bond portfolio modeling techniques,”Journal of Portfolio Management, Fall (1990) 37–48.
[13] M. Holmer, ”The asset/liability management strategy system at Fannie Mae,”Interfaces 24(3) (1994) 3–21.
[14] M.R. Holmer and S.A. Zenios, ”The productivity of financial intermediation and the technology of financial product management,”Operations Research 43(6) (1995) 970–982.
[15] J.E. Ingersoll, Jr.,Theory of Financial Decision Making, Studies in Financial Economics (Rowman & Littlefield, 1987).
[16] J.G. Kallberg, R.W. White and W.T. Ziemba, ”Short term financial planning under uncertainty,”Management Science 28(6) (1982) 670–682. · Zbl 0482.90054
[17] P. Kang and S.A. Zenios, ”Complete prepayment models for mortgage-backed securities,”Management Science 38(11) (1992) 1665–1685.
[18] M.I. Kusy and W.T. Ziemba, ”A bank asset and liability management model,”Operations Research 34 (3) (1986) 356–376.
[19] L.C. MacLean, W.T. Ziemba and G. Blazenko, ”Growth versus security in dynamic investment analysis,”Management Science 38(11) (1992) 1562–1585. · Zbl 0765.90014
[20] J. Mossin, ”Optimal multiperiod portfolio policies,”Journal of Business 41 (1968) 215–229.
[21] J.M. Mulvey and H. Vladimirou, ”Stochastic network programming for financial planning problems,”Management Science 38 (11) (1992) 1642–1664. · Zbl 0825.90062
[22] J.M. Mulvey and S.A. Zenios, ”Diversifying fixed-income porfolios: Modeling dynamics effects,”Financial Analysts Journal, January/February (1994) 30–38.
[23] S.S. Nielsen and S.A. Zenios, ”Solving multistage stochastic network programs on massively parallel computers,”Mathematical Programming 73(3) (1996) 227–250. · Zbl 0852.90111
[24] K.J. Worzel, C. Vassiadou-Zeniou and S.A. Zenios, ”Integrated simulation and optimization models for tracking indices of fixed-income securities,”Operations Research 42(2) (1994) 223–233. · Zbl 0925.90026
[25] S.A. Zenios, ”A model for portfolio management with mortgage-backed securities,”Annals of Operations Research 43 (1993) 337–356. · Zbl 0783.90014
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.