Optimal investment in derivative securities

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Optimal investment in derivative securities

Author Info

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)
Peter Carr () (Banc of America Securities, 9 West 57th Street, 40th floor, New York, N.Y. 10019, USA)

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.

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Publisher Info
Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 5 (2001)
Issue (Month): 1 ()
Pages: 33-59
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:spr:finsto:v:5:y:2001:i:1:p:33-59

Note: received: November 1999; final version received: February 2000
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Find related papers by JEL classification:
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis

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Jakša Cvitanić & Vassilis Polimenis & Fernando Zapatero, 2008. "Optimal portfolio allocation with higher moments," Annals of Finance, Springer, vol. 4(1), pages 1-28, January. [Downloadable!] (restricted)
Liu, Jun & Pan, Jun, 2003. "Dynamic Derivative Strategies," Working papers 4334-02, Massachusetts Institute of Technology (MIT), Sloan School of Management. [Downloadable!]

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