A C\`adl\`ag Rough Path Foundation for Robust Finance
| Autor: | Allan, Andrew L., Liu, Chong, Prömel, David J. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Finance Stoch. 28 (2024), no.1, 215--257 |
| Druh dokumentu: | Working Paper |
| Popis: | Using rough path theory, we provide a pathwise foundation for stochastic It\^o integration, which covers most commonly applied trading strategies and mathematical models of financial markets, including those under Knightian uncertainty. To this end, we introduce the so-called Property (RIE) for c\`adl\`ag paths, which is shown to imply the existence of a c\`adl\`ag rough path and of quadratic variation in the sense of F\"ollmer. We prove that the corresponding rough integrals exist as limits of left-point Riemann sums along a suitable sequence of partitions. This allows one to treat integrands of non-gradient type, and gives access to the powerful stability estimates of rough path theory. Additionally, we verify that (path-dependent) functionally generated trading strategies and Cover's universal portfolio are admissible integrands, and that Property (RIE) is satisfied by both (Young) semimartingales and typical price paths. Comment: 35 pages |
| Databáze: | arXiv |
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