2007/06/04 by Mark Owen, Mark P. Owen, Owen, Mark +3
Economics, Econometrics and Finance · Mathematics · #91B16 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Primary 91B28 #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR #msc:91B16 #msc:91B28 #q-fin.PM
paper · pdf · doi:10.48550/arxiv.0706.0478
major revision (mostly, but not entirely, cosmetic)
openalex publication_date 2007/06/04 · arxiv created 2007/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.