{"ID":2838345,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.18169","arxiv_id":"2511.18169","title":"Superhedging under Proportional Transaction Costs in Continuous Time","abstract":"We revisit the well-studied superhedging problem under proportional transaction costs in continuous time using the recently developed tools of set-valued stochastic analysis. By relying on a simple Black-Scholes-type market model for mid-prices and using continuous trading schemes, we define a dynamic family of superhedging sets in continuous time and express them in terms of set-valued integrals. We show that these sets, defined as subsets of Lebesgue spaces at different times, form a dynamic set-valued risk measure with multi-portfolio time-consistency. Finally, we transfer the problem formulation to a path-space setting and introduce approximate versions of superhedging sets that will involve relaxing the superhedging inequality, the superhedging probability, and the solvency requirement for the superhedging strategy with a predetermined error level. In this more technical framework, we are able to relate the approximate superhedging sets at different times by means of a set-valued Bellman's principle, which we believe will pave the way for a set-valued differential structure that characterizes the superhedging sets.","short_abstract":"We revisit the well-studied superhedging problem under proportional transaction costs in continuous time using the recently developed tools of set-valued stochastic analysis. By relying on a simple Black-Scholes-type market model for mid-prices and using continuous trading schemes, we define a dynamic family of superhe...","url_abs":"https://arxiv.org/abs/2511.18169","url_pdf":"https://arxiv.org/pdf/2511.18169v1","authors":"[\"Atiqah Almuzaini\",\"Çağın Ararat\",\"Jin Ma\"]","published":"2025-11-22T19:49:14Z","proceeding":"q-fin.RM","tasks":"[\"q-fin.RM\",\"math.OC\",\"math.PR\"]","methods":"[\"Large Language Model\"]","has_code":false}