Optimal investment in derivative securities

Dilip B. Madan (), Xing Jin () and Peter Carr
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Dilip B. Madan: Robert H. Smith School of Business, Van Munching Hall, University of Maryland, College Park, MD. 20742, USA Manuscript
Xing Jin: Robert H. Smith School of Business, Van Munching Hall, University of Maryland, College Park, MD. 20742, USA Manuscript

Finance and Stochastics, 2001, vol. 5, issue 1, 33-59

Abstract: We consider the problem of optimal investment in a risky asset, and in derivatives written on the price process of this asset, when the underlying asset price process is a pure jump Lévy process. The duality approach of Karatzas and Shreve is used to derive the optimal consumption and investment plans. In our economy, the optimal derivative payoff can be constructed from dynamic trading in the risky asset and in European options of all strikes. Specific closed forms illustrate the optimal derivative contracts when the utility function is in the HARA class and when the statistical and risk-neutral price processes are in the variance gamma (VG) class. In this case, we observe that the optimal derivative contract pays a function of the price relatives continuously through time.

Keywords: Lévy process; market completeness; stochastic duality; option pricing; variance gamma model (search for similar items in EconPapers)
JEL-codes: C61 G11 (search for similar items in EconPapers)
Date: 2001-01-10
Note: received: November 1999; final version received: February 2000
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Citations: View citations in EconPapers (13)

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