2017/10/12 by Lingqi Gu, Gu, Lingqi, Yiqing Lin +3
Decision Sciences · Economics, Econometrics and Finance · #60G48 #91G80 #93E15 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1710.04363
openalex publication_date 2017/10/12 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
This paper discusses the num 'eraire-based utility maximization problem in\nmarkets with proportional transaction costs. In particular, the investor is\nrequired to liquidate all her position in stock at the terminal time. We first\nobserve the stability of the primal and dual value functions as well as the\nconvergence of the primal and dual optimizers when perturbations occur on the\nutility function and on the physical probability. We then study the properties\nof the optimal dual process (ODP), that is, a process from the dual domain that\ninduces the optimality of the dual problem. When the market is driven by a\ncontinuous process, we construct the ODP for the problem in the limiting market\nby a sequence of ODPs corresponding to the problems with small misspecificated\nparameters. Moreover, we prove that this limiting ODP defines a shadow price.\n