Optimal Portfolio for CRRA Utility Functions When Risky Assets are Exponential Additive Processes

26 Pages Posted: 1 Nov 2010

See all articles by Tiziano Vargiolu

Tiziano Vargiolu

University of Padua - Department of Pure and Applied Mathematics

Laura Pasin

affiliation not provided to SSRN

Abstract

In this paper, we analyse a market where the risky assets follow exponential additive processes, which can be viewed as time-inhomogeneous generalizations of geometric Levy processes. In this market we show that, when an investor wants to maximize a CRRA utility function of his/her terminal wealth, his/her optimal strategy consists in keeping proportions of wealth in the risky assets which depend only on time but not on the current wealth level or on the prices of the risky assets. In the time-homogeneous case, the optimal strategy is to keep constant proportions of wealth, a result already found by Kallsen which extends the classical Merton’s result to this market. While the one-dimensional case has been extensively treated and the multidimensional case has been treated only in the time-homogeneous case Callegaro and Vargiolu (2009), Kallsen (2000), and Korn et al. (2003) to the authors’ knowledge this is the first time that such results are obtained for exponential additive processes in the multidimensional case. We use these results to show that the optimal solution in the presence of jumps has the form of the analogous one without jumps but with the asset yields vector reduced by suitable quantities: in the one-dimensional case, we extend a result by Benth et al. (2001). We conclude with four examples.

Suggested Citation

Vargiolu, Tiziano and Pasin, Laura, Optimal Portfolio for CRRA Utility Functions When Risky Assets are Exponential Additive Processes. Economic Notes, Vol. 39, Issue 1-2, pp. 65-90, February / July 2010. Available at SSRN: https://ssrn.com/abstract=1700305 or http://dx.doi.org/10.1111/j.1468-0300.2010.00222.x

Tiziano Vargiolu (Contact Author)

University of Padua - Department of Pure and Applied Mathematics ( email )

Via Belzoni 7
Padova, 35100
ITALY

Laura Pasin

affiliation not provided to SSRN

No Address Available

Register to save articles to
your library

Register

Paper statistics

Downloads
2
Abstract Views
612
PlumX Metrics