Optimal investment in derivative securities

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2001Publisher:Springer Science and Business Media LLCJournal:Finance and Stochastics, volume 5, pages 33-59 (issn: 0949-2984, eissn: 1432-1122,

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Authors: Dilip B. Madan; Xing Jin; Peter Carr;

doi: 10.1007/s007800000023

Optimal investment in derivative securities

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Abstract

The authors consider the problem of the optimal investment in a risky asset and some derivatives. The case of underlying asset price process which is a pure jump Lévy process is considered. The martingale representation theorem, description of self-financial strategies and budget constraint are given. The finite and infinite horizon consumption and investment problems are considered. Explicit solutions for the case of HARA (hyperbolic absolute risk aversion) utility are presented.

Related Organizations

University of Maryland, College Park
United States
University of Maryland, College Park
United States

Keywords

Lévy process, Dynamic programming in optimal control and differential games, Lévy process, market completeness, stochastic duality, option pricing, variance gamma model, Martingales with continuous parameter, variance gamma model, market completeness, stochastic duality, Jump processes, option pricing, jel: jel:C61, jel: jel:G11

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