53 citations · 55 across the 5 of their papers we have counts for
5 papers · 1 filter
Generalized Multivariate Hawkes Processes
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Nieweglowski
This work contributes to the theory and applications of Hawkes processes. We introduce and examine a new class of Hawkes processes that we call generalized Hawkes processes, and th…
Wiener-Hopf Factorization for Time-Inhomogeneous Markov Chains
Tomasz R. Bielecki, Ziteng Cheng, Igor Cialenco +1
This work contributes to the theory of Wiener-Hopf type factorization for finite Markov chains. This theory originated in the seminal paper Barlow et al. (1980), which treated the…
Semimartingales and Shrinkage of Filtration
Tomasz R. Bielecki, Jacek Jakubowski, Monique Jeanblanc +1
We consider a complete probability space , which is endowed with two filtrations, and , assumed to satisfy the usual conditions…
Wiener-Hopf factorization for time-inhomogeneous Markov chains and its application
Tomasz R. Bielecki, Igor Cialenco, Ruoting Gong +1
In this paper we derive the Wiener-Hopf factorization for a finite-state time-inhomogeneous Markov chain. To the best of our knowledge, this study is the first attempt to investiga…
Pricing and trading credit default swaps in a hazard process model
Tomasz R. Bielecki, Monique Jeanblanc, Marek Rutkowski
In the paper we study dynamics of the arbitrage prices of credit default swaps within a hazard process model of credit risk. We derive these dynamics without postulating that the i…