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Optimal investment strategies in the presence of a minimum guarantee. (English) Zbl 1074.91013
This research paper represents a significant study in obtaining optimal strategies in a model for a defined contribution pension fund, taking into account the presence of a minimum guarantee and a continuous-time framework. This kind of long-term investment problems allows for a stochastic term structure concerning the interest rates and it is related to the pension fund management. The authors completed this work with a pertinent numerical analysis, important comparisons and they suggest several directions for future research using the final conclusions and the appropriate references.

91B28Finance etc. (MSC2000)
Full Text: DOI
[1] Bajeux-Besnainou, I., Jordan, J.V., Portait, R., 1998. Dynamic asset allocation for stocks, bonds and cash over long horizons. In: Presented at the 1998 Southern Finance Association Conference and at the October 1998 Bachelier Seminar in Paris. · Zbl 1011.91040
[2] Bajeux-Besnainou, I., Jordan, J.V., Portait, R., 1999. On the bond-stock asset allocation puzzle. In: Presented at the 1999 Eastern Finance Association Conference. · Zbl 1011.91040
[3] Boulier, J. F.; Huang, S. J.; Taillard, G.: Optimal management under stochastic interest rates: the case of a protected pension fund. Insurance: mathematics and economics 28, 173-189 (2001) · Zbl 0976.91034
[4] Chan, K. C.; Karolyi, G. A.; Longstaff, F. S.; Sanders, A. B.: The volatility of short-term interest rates: an empirical comparison of alternative models of the term structure of interest rates. Journal of finance 47, 1209-1227 (1992) · Zbl 1065.91505
[5] Cox, J.; Huang, C. F.: Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of economic theory 49, 33-83 (1989) · Zbl 0678.90011
[6] Cox, J.; Ingersoll, J. E.; Ross, S. A.: A theory of the term structure of interest rates. Econometrica 53, 385-408 (1985) · Zbl 1274.91447
[7] Deelstra, G.; Grasselli, M.; Koehl, P. F.: Optimal investment strategies in a CIR framework. Journal of applied probability 37, 1-12 (2000) · Zbl 0989.91040
[8] Duffie, D.; Kan, R.: A yield-factor model of interest rates. Mathematical finance 6, 379-406 (1996) · Zbl 0915.90014
[9] El Karoui, N.; Jeanblanc-Picqué, M.: Optimization and consumption with labor income. Finance and stochastics 2, 409-440 (1998) · Zbl 0930.60050
[10] Jensen, B.A., Sørensen, C., 2000. Paying for minimum interest rate guarantees: Who should compensate who? European Financial Management, Vol. 7.
[11] Karatzas, I.: Optimization problems in the theory of continuous trading. SIAM journal of control and optimization 27, 1221-1259 (1989) · Zbl 0701.90008
[12] Karatzas, I., Shreve, S., 1990. Brownian Motion and Stochastic Calculus. Springer, Berlin. · Zbl 0734.60060
[13] Karatzas, I.; Lehoczky, J. P.; Shreve, S.: Optimal portfolio and consumption decisions for a ”small investor” on a finite horizon. SIAM journal of control and optimization 25, 1557-1586 (1987) · Zbl 0644.93066
[14] Lamberton, D., Lapeyre, B., 1991. Introduction au calculstochastique appliqué à la finance, Mathématiques et Applications, Ellipses, Paris.
[15] Lioui, A.; Poncet, P.: On optimal portfolio choice under stochastic interest rates. Journal of economic dynamics and control 25, 1841-1865 (2001) · Zbl 0979.91032
[16] Merton, R., 1971. Optimum comsumption and portfolio rules in a continuous-time case, Journal of Economic Theory 3, 373--413; erratum: 6 (1973) 213--214. · Zbl 1011.91502
[17] Pitman, J.; Yor, M.: A decomposition of Bessel bridges. Z. wahrscheinlichkeistheorie verw. Gebiete 59, 425-457 (1982) · Zbl 0484.60062
[18] Vasiček, O. A.: An equilibrium characterization of the term structure. Journal of financial economics 5, 177-188 (1977)