Kassis, Georges;
Macrina, Andrea;
(2022)
Arcade Processes and Martingale Interpolation.
ArXiv: Ithaca, NY, USA.
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Abstract
Arcade processes are a class of continuous stochastic processes that interpolate in a strong-sense, i.e., omega by omega, between zeros at fixed pre-specified times. Their additive randomization allows one to match any given random variable at the given dates on the whole probability space, and can be interpreted as a generalization of anticipative stochastic bridges. The filtrations generated by randomized arcade processes are utilized to construct a class of interpolating martingales between the same target random variables, the filtered arcade martingales (FAMs), which provide an extension to the paradigm of information-based asset pricing. FAMs are strong solutions of the martingale fitting problem, and can be connected to martingale optimal transport (MOT) by considering optimally-coupled target random variables. Another connection to optimal transport can be established by using FAMs to cast the information-based martingale optimal transport problem, a new problem that allows the introduction of noise in MOT, similar to how Schrödinger's problem introduces noise in optimal transport.
| Type: | Working / discussion paper |
|---|---|
| Title: | Arcade Processes and Martingale Interpolation |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://arxiv.org/abs/2301.05936 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Stochastic interpolation, Martingale interpolation, Stochastic bridge, Information-based asset pricing, Nonlinear stochastic filtering,, Optimal transport |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10156381 |
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