In this paper we study ergodicity and related semigroup property for a class of symmetric Markov jump processes associated with time-changed symmetric α-stable processes. For this purpose, explicit and sharp criteria for Poincaré type inequalities (including Poincaré, super Poincaré and weak...

We study a mixed hitting-time (MHT) model that specifies durations as the first time a Lévy process— a continuous-time process with stationary and independent increments— crosses a heterogeneous threshold. Such models are of substantial interest because they can be reduced from...

The paper focuses on the option price subdiffusive model under the unusual behavior of the market, when the price may not be changed for some time which is quite a common situation in the modern financial markets or during global crises. In the model, the risk-free bond motion and classical GBM...

A credit default swap (CDS) is a financial contract in which the holder of the instrument will be compensated in the event of a loan default. When available, CDS's are used to monitor the credit risk of countries and companies. In this work we develop a closed form procedure to value a CDS in...

We study a mixed hitting-time (MHT) model that specifies durations as the first time a Lévy process - a continuous-time process with stationary and independent increments - crosses a heterogeneous threshold. Such models are of substantial interest because they can be reduced from...