On the stability of the martingale optimal transport problem: A set-valued map approach
| Autor: | Ariel Neufeld, Julian Sester |
|---|---|
| Přispěvatelé: | School of Physical and Mathematical Sciences |
| Rok vydání: | 2021 |
| Předmět: |
Mathematics [Science]
Statistics and Probability Stability (learning theory) Hemicontinuity 01 natural sciences Set (abstract data type) FOS: Economics and business 010104 statistics & probability Perspective (geometry) FOS: Mathematics Applied mathematics Martingale Optimal Transport 0101 mathematics Mathematics - Optimization and Control Real line Mathematics 010102 general mathematics Probability (math.PR) Mathematical Finance (q-fin.MF) Compact space Quantitative Finance - Mathematical Finance Optimization and Control (math.OC) Statistics Probability and Uncertainty Martingale (probability theory) Stability Value (mathematics) Mathematics - Probability |
| DOI: | 10.48550/arxiv.2102.02718 |
| Popis: | Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer (2019) and Wiesel (2019). We present a new perspective of this result using the theory of set-valued maps. In particular, using results from Beiglböck et al. (2021), we show that the set of martingale measures with fixed marginals is continuous, i.e., lower- and upper hemicontinuous, w.r.t. its marginals. Moreover, we establish compactness of the set of optimizers as well as upper hemicontinuity of the optimizers w.r.t. the marginals. Nanyang Technological University Financial support by the Nanyang Assistant Professorship, Singapore Grant (NAP Grant) Machine Learning based Algorithms in Finance and Insurance is gratefully acknowledged. |
| Databáze: | OpenAIRE |
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