2011/12/11 by Dmitry B. Rokhlin, Rokhlin, Dmitry B. · 1 citation
Economics, Econometrics and Finance · #49K35 #91A30 #91G10 #Economic Theory and Institutions #Economic theories and models #FOS: Economics and business #Portfolio Management (q-fin.PM) #Stochastic processes and financial applications #msc:49K35 #msc:91A30 #msc:91G10 #q-fin.PM
paper · pdf · doi:10.48550/arxiv.1112.2406
19 pages, minor corrections, Example 5 is added
openalex publication_date 2011/12/11 · arxiv created 2011/12/19 · arxiv updated 2011/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To any utility maximization problem under transaction costs one can assign a frictionless model with a price process S^*, lying in the bid/ask price interval [\underline S, S]. Such process S^* is called a shadow price if it provides the same optimal utility value as in the original model with bid-ask spread. We call S^* a generalized shadow price if the above property is true for the relaxed utility function in the frictionless model. This relaxation is defined as the lower semicontinuous envelope of the original utility, considered as a function on the set [\underline S, S], equipped with some natural weak topology. We prove the existence of a generalized shadow price under rather weak assumptions and mark its relation to a saddle point of the trader/market zero-sum game, determined by the relaxed utility function. The relation of the notion of a shadow price to its generalization is illustrated by several examples. Also, we briefly discuss the interpretation of shadow prices via Lagrange duality.