Skorokhod Transition in the Conic Market Model

2025/09/04 by Sidorenko, Artur
#60H30 (Primary) #91G10 (Secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2509.04608

Abstract

This paper examines the applicability of the Skorokhod representation theorem in filtrated probability spaces for the utility maximization problem in the Kabanov conic model of multi-asset markets with proportional transaction costs. A key challenge is that the theorem does not necessarily preserve adaptedness, meaning that solutions obtained on an auxiliary probability space may not correspond to those on the original one. We establish that, under mild conditions, the Bellman functionals remain consistent across different probability spaces.

Citations

• The randomization method in stochastic optimal control
• Extended Weak Convergence and Utility Maximization with Proportional\n Transaction Costs
• Behavioural investors in conic market models
• Skorohod's representation theorem and optimal strategies for markets\n with frictions

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