Optimal Consumption and Investment for Exponential Utility Function

Year 2017, Volume: 5 Issue: 1, 19 - 26, 30.04.2017

Faiza Limam_belarbi Fatima Zohra Tahraoui

https://doi.org/10.36753/mathenot.421478

Cited By: 1

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.

Keywords

Portfolio optimization, consumption, exponential utility Convex duality

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.