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Optimal investment strategies in a CIR framework

Published online by Cambridge University Press:  14 July 2016

Griselda Deelstra ,
Martino Grasselli  and
Pierre-François Koehl
Griselda Deelstra*
Affiliation:
CREST and ENSAE
Martino Grasselli*
Affiliation:
CREST
Pierre-François Koehl*
Affiliation:
CDC and DABF
*
∗ Postal address: Centre for Research in Economics and Statistics, Finance Department, 15 Boulevard Gabriel Péri, 92245 Malakoff Cedex, France.
∗ Postal address: Centre for Research in Economics and Statistics, Finance Department, 15 Boulevard Gabriel Péri, 92245 Malakoff Cedex, France.
∗∗∗ Postal address: Caisse des Dépôts et Consignations, Direction des Activités Bancaires et Financières, Paris, France.
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Abstract

We study an optimal investment problem in a continuous-time framework where the interest rates follow Cox-Ingersoll-Ross dynamics. Closed form formulae for the optimal investment strategy are obtained by assuming the completeness of financial markets and the CRRA utility function. In particular, we study the behaviour of the solution when time approaches the terminal date.

Keywords

Consumption-investment strategystochastic interest ratesstochastic optimization
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 936 - 946
Copyright
Copyright © by the Applied Probability Trust 2000 

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Footnotes

The views expressed in this paper are those of the authors and do not reflect those of the CDC.

References

Bajeux-Besnainou, I., Jordan, J. V., and Portait, R. (1998). Dynamic asset allocation for stocks, bonds and cash over long horizons. Presented at the 1998 Southern Finance Association conference and at the October 1998 Bachelier Seminar, Paris.Google Scholar
Bajeux-Besnainou, I., Jordan, J. V., and Portait, R. (1999). On the bond–stock asset allocation puzzle. Presented at the 1999 Eastern Finance Association Conference.Google Scholar
Cox, J., and Huang, C. F. (1989). Optimal consumption and portfolio policies when asset prices follow a diffusion process. J. Econ. Theory 49, 33–83.Google Scholar
Cox, J., and Huang, C. F. (1991). A variational problem arising in financial economics. J. Math. Econ. 20, 465–487.Google Scholar
Cox, J. C., Ingersoll, J. E., and Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica 53, 385–408.CrossRefGoogle Scholar
Karatzas, I. (1989). Optimization problems in the theory of continuous trading. SIAM. J. Control Optimization 27, 1221–1259.CrossRefGoogle Scholar
Karatzas, I., Lehoczky, J. P., and Shreve, S. (1987). Optimal portfolio and consumption decisions for a ‘small investor’ on a finite horizon. SIAM. J. Control Optimization 25, 1557–1586.Google Scholar
Lamberton, D., and Lapeyre, B. (1991). Introduction au calcul stochastique appliqué à la finance. Ellipses, Paris.Google Scholar
Long, J. B. (1990). The numeraire portfolio. J. Financial Econ. 26, 29–69.Google Scholar
Merton, R. C. (1971). Optimum consumption and portfolio rules in a continuous-time case. J. Econ. Theory 3, 373–413. Erratum: ibid. 6 (1973), 213–214.Google Scholar
Merton, R. (1992). Continuous Time Finance. Blackwell, Oxford.Google Scholar
Pitman, J., and Yor, M. (1982). A decomposition of Bessel bridges. Z. Wahrscheinlichkeitsth. 59, 425–457.Google Scholar
Rogers, L. C. G. (1995). Which model for term-structure of interest rates should one use? In IMA Vol. 65: Mathematical Finance, eds Davis, M. H. A. et at. Springer, New York, pp. 93–116.Google Scholar
Sørensen, C. (1999). Dynamic asset allocation and fixed income management. J. Financial Quant. Anal. 34, 513–531.Google Scholar