5 papers
Scaling limits of Lévy walks with random velocities
Hubert Woszczek, Marek A. Teuerle, Agnieszka Wyłomańska
This paper investigates Lévy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depe…
Asymmetric Lévy walks driven by convex combination of fractional material derivatives
Łukasz Płociniczak, Marek A. Teuerle, Hubert Woszczek
We analyze a class of linear partial differential equations that arise as deterministic descriptions of the scaling limits of Lévy walks, in which transport is driven by a convex c…
Modelling and valuation of catastrophe bonds across multiple regions
Krzysztof Burnecki, Marek Teuerle, Martyna Zdeb
The insurance-linked securities (ILS) market, as a form of alternative risk transfer, has been at the forefront of innovative risk-transfer solutions. The catastrophe bond (CAT bon…
Design and valuation of multi-region CoCoCat bonds
Jacek Wszoła, Krzysztof Burnecki, Marek Teuerle +1
This paper introduces a novel multidimensional insurance-linked instrument: a contingent convertible bond (CoCoCat bond) whose conversion trigger is activated by predefined natural…
Fractional material derivative: pointwise representation and a finite volume numerical scheme
Łukasz Płociniczak, Marek A. Teuerle
The fractional material derivative appears as the fractional operator that governs the dynamics of the scaling limits of Lévy walks - a stochastic process that originates from the…