zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Optimal management under stochastic interest rates: The case of a protected defined contribution pension fund. (English) Zbl 0976.91034
Summary: This paper deals with the pension fund management issue. We focus on defined-contribution plans where a guarantee is given on the benefits, and the guarantee depends on the level of the stochastic interest rate when the employee retires. It is particularly shown that the optimal composition of this kind of pension fund can be divided into three different parts: a loan which amounts to the present value of the contributions, a contingent claim delivering the guarantee and a hedging fund. A Vasicek interest rate model is considered as an illustration of our analysis.

91B28Finance etc. (MSC2000)
Full Text: DOI
[1] Bajeux-Besnainou, I., Portait, R., 1998. Dynamic asset allocation in a mean-variance framework. Management Science. · Zbl 1011.91040
[2] Bajeux-Besnainou, I., Portait, R., 1999. L’allocation stratégique d’actifs: l’apport de nouveaux modèles d’optimisation de portfeuilles. ESSEC Working Paper.
[3] Bielecki, T. R.; Pliska, S. R.: Risk-sensitive dynamic asset allocation. Asset and liability management 8, 129-138 (1998) · Zbl 0984.91047
[4] Black, F.; Perold, A.: Theory of constant proportion portfolio insurance. Journal of economic dynamics and control 16, 403-426 (1992) · Zbl 0825.90056
[5] Bodie, Z.; Crane, D. B.: The design and production of new retirement savings products. The journal of portfolio management 25, 77-82 (1999)
[6] Bodie, Z.; Merton, R. C.; Samuelson, W. F.: Labor supply flexibility and portfolio choice in a life cycle model. Journal of economic dynamics and control 3--4, No. 16, 427-449 (1992)
[7] Booth, P.M., 1995. The management of investment risk for defined contribution pension scheme. Transactions of 25th International Congress of Actuaries.
[8] Booth, P.M., Yakoubov, Y.Y., 2000. Investment policy for defined contribution pension schemes close to retirement: An analysis of the ’Life Cycle’ concept. North American Actuarial Journal, in press. · Zbl 1083.91527
[9] Boulier, J.F., 1996a. Modèle simplifie d’allocation en actions des fonds de pension. Gestion Collective Internationale.
[10] Boulier, J.F., 1996b. Gestion actif-passif des fonds de pension. La Revue de l’AFPEN No. 2.
[11] Brennan, M. J.; Schwartz, E. S.; Lagnado, R.: Strategic asset allocation. Journal of economic dynamics and control 21, No. 8--9, 1377-1403 (1997) · Zbl 0901.90008
[12] Clup, C., Tanner, K., Mensink, R., 1997. Returns and Retirement, Risk 10, No. 10.
[13] Davis, E.P., 1995. Pension Funds: Retirement-income Security and Capital Markets: An International Perspective. Oxford University Press, Oxford.
[14] El Karoui, N., 1998. Modèles de taux d’intérêt. Cours de DEA, Laboratoire de Probabilités et Modèles Aléatoires de l’Université, Paris VI.
[15] El Karoui, N., Huang, S.J., 1997. A General Results of Existence and Uniqueness of Backward Stochastic Differential Equations. Pitman Research Notes in Mathematical Series No. 364. Longman, New York, pp. 26--36. · Zbl 0887.60064
[16] El Karoui, N., Huang, S.J., 1998. Some results on a general class of backward stochastic differential equations and application in finance. Working Paper.
[17] Fitoussi, J.P., 1999. Introduction au dossier sur les retraites: un débat pour progresser. Observatoire Français des Conjonctures Economiques Presses de Sciences Politiques 68, pp. 9--14.
[18] Kapur, S., Orszag, J.M., 1999. A portfolio approach to investment and annuitization during retirement. In: Proceedings of the Third International Congress on ’Insurance: Mathematics and Economics’, London.
[19] Kaye, G.D., 1985. Taxation of pension funds. Research Report in City University.
[20] Khorasanee, M. Z.: A pension plan incorporation both defined benefit and defined contribution principles. Journal of actuarial practice 3, No. 2, 269-300 (1996) · Zbl 1060.91063
[21] Khorasanee, M. Z.: Deterministic modeling of defined-contribution pension fund. North American actuarial journal 1, No. 4, 83-103 (1997) · Zbl 1080.91521
[22] Markowitz, H.M., 1991. Portfolio Selection: Efficient Diversification of Investments, 2nd Edition. Blackwell, Cambridge, MA.
[23] Merton, R.: Optimum consumption and portfolio rules in a continuous-time model. Journal of economic theory 3, 373-413 (1971) · Zbl 1011.91502
[24] Pardoux, E.; Peng, S.: Adapted solution of a backward stochastic differential equation. Systems and control letters 14, 55-61 (1990) · Zbl 0692.93064
[25] Pochart, C., Taillard, G., Veltman, H., 1997. Defined contribution pension funds, Quants 27. Crédit Commércial de France.
[26] Verrall, R., Yakoubov, 1999. A fuzzy approach to grouping by policyholder age in general insurance. Journal of Actuarial Practice, in press. · Zbl 1070.91511