Stochastic Control and Levy Processes for Systematic Trading

In systematic decision making in quantitative finance, stochastic optimal control provide a ramework for capturing market randomness and the progressive revelation of information. To complement this, Lévy processes, which have stationary, independent increments, provide a unified parametric to modeling evolving quantities such as asset prices and insurance claim sizes. edit use own wording! this is not blogging otherwise

Under the guiding supervision of Dr. Jingyi Cao, I presented a seminar on this topic during my Master’s, focusing on the paper “Optimally Stopping at a Given Distance from the Ultimate Supremum of a Spectrally Negative Lévy Process” by Mónica B. Carvajal Pinto and Kees van Schaik, which I will discuss here. In a future post, I may explore more recent developments in the field, such as Baurdoux and Pedraza’s “On the Last Zero Process with an Application in Corporate Bankruptcy.”

For a given Lévy process $(X_t){t \ge 0}$ defined on the filtered probability space ((\Omega, \mathcal{F}, (\mathcal{F}_t){t \ge 0}, \mathbb{P})) …