Zeitraum: 14.01.2016 16:15 Uhr - 18:00 Uhr
Ort: Carl-Zeiss-Straße 3, SR 384
A-transform, its properties and some applications
Abstract: Here we introduce the so-called A-transform built on some random variable η. The A-transform, if applied to a monomial, results in a well-known Appell polynomial. Not surprisingly, the transformed function has properties similar to an Appell polynomial. For example,
the transformed function is a martingale if the transform is built on a Lévy process. As a consequence of the above, the A-transform is especially useful for solving problems related to Lévy processes. For instance, it gives a straightforward formula for the calculation of martingales with given boundary conditions. In the context of optimal stopping, one can obtain an optimal stopping rule by studying the geometrical properties of the transformed payoff. If compared to the standard approach, the A-transform method benefits from the absence of integro-differential equations, making the process of obtaining the solution much easier. We illustrate the method with some examples.
If we have time, we shall also discuss the connection between the A-transform and the Wick product.
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Ilya Pavlyukevich /Professur für Stochastik mit Anwendungen in den Naturwissenschaften / Institut für Mathematik / Ernst-Abbe-Platz 2 / 07743 Jena