2014/08/26 by Christoph Czichowsky, Czichowsky, Christoph, Walter Schachermayer +3 · 1 citation
Economics, Econometrics and Finance · #60G48 #91G10 #93E20 #Capital Investment and Risk Analysis #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1408.6065
openalex publication_date 2014/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e.~a least favorable frictionless market leading to the same optimal strategy and utility as in the original market under transaction costs. The crucial ingredients are the continuity of the price process and the hypothesis of "no unbounded profit with bounded risk". A counter-example reveals that these hypotheses cannot be relaxed.