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Year 2017, Volume: 5 Issue: 1, 19 - 26, 30.04.2017
https://doi.org/10.36753/mathenot.421478

Abstract

References

  • [1] Karatzas, I. and Shreve, S.E., Methods of Mathematical Finance. Springer, Berlin, 1998.
  • [2] Korn, R., Optimal portfolios. World Scientific, Singapore, 1997.
  • [3] Kluppelberg, C. and Pergamenchtchikov, S., Optimal consumption and investment with bounded downside risk for power utility functions. Optimality and Risk - Modern Trends in Mathematical Finance. (2010), 133-170.
  • [4] Rockafellar, R.T., Convex Analysis. Princeton University Press, Princeton, NJ 1970.
  • [5] Ekeland, I. and Temam, R., Convex Analysis and Variational Problems. North Holland, Amsterdam and American Elsevier, New York (1976).
  • [6] Xu, G.L., A duality method for optimal consumption and investment under short-selling prohibition. Doctoral dissertation, Department of Mathematics, Carnegie-Mellon University, 1990.

Optimal Consumption and Investment for Exponential Utility Function

Year 2017, Volume: 5 Issue: 1, 19 - 26, 30.04.2017
https://doi.org/10.36753/mathenot.421478

Abstract

We investigate an optimal consumption and investment problem for Black-Scholes type financial market
on the whole investment interval [0, T]. We formulate various utility maximization problem, which can
be solved explicitly. The method of solution uses the convex dual function (Legendre transform) of the
utility function. Related to this concept, we introduce and study the convex dual of the value function for
our problem.

References

  • [1] Karatzas, I. and Shreve, S.E., Methods of Mathematical Finance. Springer, Berlin, 1998.
  • [2] Korn, R., Optimal portfolios. World Scientific, Singapore, 1997.
  • [3] Kluppelberg, C. and Pergamenchtchikov, S., Optimal consumption and investment with bounded downside risk for power utility functions. Optimality and Risk - Modern Trends in Mathematical Finance. (2010), 133-170.
  • [4] Rockafellar, R.T., Convex Analysis. Princeton University Press, Princeton, NJ 1970.
  • [5] Ekeland, I. and Temam, R., Convex Analysis and Variational Problems. North Holland, Amsterdam and American Elsevier, New York (1976).
  • [6] Xu, G.L., A duality method for optimal consumption and investment under short-selling prohibition. Doctoral dissertation, Department of Mathematics, Carnegie-Mellon University, 1990.
There are 6 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Faiza Limam_belarbi This is me

Fatima Zohra Tahraoui This is me

Publication Date April 30, 2017
Submission Date October 26, 2015
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Limam_belarbi, F., & Tahraoui, F. Z. (2017). Optimal Consumption and Investment for Exponential Utility Function. Mathematical Sciences and Applications E-Notes, 5(1), 19-26. https://doi.org/10.36753/mathenot.421478
AMA Limam_belarbi F, Tahraoui FZ. Optimal Consumption and Investment for Exponential Utility Function. Math. Sci. Appl. E-Notes. April 2017;5(1):19-26. doi:10.36753/mathenot.421478
Chicago Limam_belarbi, Faiza, and Fatima Zohra Tahraoui. “Optimal Consumption and Investment for Exponential Utility Function”. Mathematical Sciences and Applications E-Notes 5, no. 1 (April 2017): 19-26. https://doi.org/10.36753/mathenot.421478.
EndNote Limam_belarbi F, Tahraoui FZ (April 1, 2017) Optimal Consumption and Investment for Exponential Utility Function. Mathematical Sciences and Applications E-Notes 5 1 19–26.
IEEE F. Limam_belarbi and F. Z. Tahraoui, “Optimal Consumption and Investment for Exponential Utility Function”, Math. Sci. Appl. E-Notes, vol. 5, no. 1, pp. 19–26, 2017, doi: 10.36753/mathenot.421478.
ISNAD Limam_belarbi, Faiza - Tahraoui, Fatima Zohra. “Optimal Consumption and Investment for Exponential Utility Function”. Mathematical Sciences and Applications E-Notes 5/1 (April 2017), 19-26. https://doi.org/10.36753/mathenot.421478.
JAMA Limam_belarbi F, Tahraoui FZ. Optimal Consumption and Investment for Exponential Utility Function. Math. Sci. Appl. E-Notes. 2017;5:19–26.
MLA Limam_belarbi, Faiza and Fatima Zohra Tahraoui. “Optimal Consumption and Investment for Exponential Utility Function”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 1, 2017, pp. 19-26, doi:10.36753/mathenot.421478.
Vancouver Limam_belarbi F, Tahraoui FZ. Optimal Consumption and Investment for Exponential Utility Function. Math. Sci. Appl. E-Notes. 2017;5(1):19-26.

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