On Feedback Trading, Stochastic Differential Equations, and Fubini’s Theorem

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Baumann, Michael Heinrich:
On Feedback Trading, Stochastic Differential Equations, and Fubini’s Theorem.
2021
Event: The 2021 INFORMS Annual Meeting , 24.-27. Okt. 2021 , Anaheim, California, United States, online.
(Conference item: Conference , Speech )

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For feedback trading strategies, which are model free and based on control techniques, many performance results are published. These results are typically obtained for specific strategies, e.g., the Simultaneously Long Short strategy or its variations, and specific underlying price dynamics such as geometric Brownian motions, Merton’s Jump Diffusion Model, abstract semimartingales, tree models. In this talk, we present results for price process definitions as they are used in finance, i.e. via (systems of) stochastic differential equations (SDEs), which might not have Brownian motions as integrators. When analyzing feedback rules on prices governed by such SDEs, calculations become more involved since Itô
integrals with non-Brownian integrators and expectations have to be interchanged. To this end, a relatively new stochastic Fubini-type theorem is presented.