Optimal Investment with an Unbounded Random Endowment and Utility-Based Pricing

Content Provider	Semantic Scholar
Author	Zitkovic, Gordan
Copyright Year	2008
Abstract	This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies – those strategies whose wealth process is a supermartingale under all pricing measures with finite relative entropy. We give necessary and sufficient conditions for the absence of utility-based arbitrage, and for the existence of a solution to the primal problem. We consider two utility-based methods which can be used to price contingent claims. Firstly we investigate marginal utility-based price processes (MUBPP’s). We show that such processes can be characterized as local martingales under the normalized optimal dual measure for the utility maximizing investor. Finally, we present some new results on utility indifference prices, including continuity properties and volume asymptotics for the case of a general utility function, unbounded endowment and unbounded contingent claims.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://arxiv.org/pdf/0706.0478v2.pdf
Language	English
Access Restriction	Open
Subject Keyword	Algorithmic trading Apathy Contingency (philosophy) Dual Duality (optimization) Expected utility hypothesis Kullback–Leibler divergence Marginal model Scott continuity Status Epilepticus
Content Type	Text
Resource Type	Article