9 citations · 21 across the 15 of their papers we have counts for
17 papers
Functional Laws of Large Numbers for Marked Hawkes Processes and Compound Marked Hawkes Processes
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz iewȩgłowski +1
We give functional laws of large numbers for a class of marked Hawkes processes and marked compound Hawkes processes with a general mark space. Our results provide some complement…
Loglinear Hawkes processes: existence, nonexplosion, stability and moment bounds
Tomasz R. Bielecki, Jacek Jakubowski, Matthias Kirchner +1
This paper discusses a special class of nonlinear Hawkes processes, where the rate function is the exponential function. We call these processes loglinear Hawkes processes. Such pr…
On Function of Evolution of Distribution for Time Homogeneous Markov Processes
Tomasz Bielecki, Jacek Jakubowski, Maciej Wiśniewolski
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of di…
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…
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…
Conditional Markov Chains Part II: Consistency and Copulae
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Niewęgłowski
In this paper we continue the study of conditional Markov chains (CMCs) with finite state spaces, that we initiated in Bielecki, Jakubowski and Niewęgłowski (2015). Here, we turn o…
Conditional Markov Chains Revisited Part I: Construction and properties
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Niewęgłowski
In this paper we continue the study of conditional Markov chains (CMCs) with finite state spaces, that we initiated in Bielecki, Jakubowski and Niewęgłowski (2014a) in an effort to…
On matching diffusions, Laplace transforms and partial differential equations
Maciej Wiśniewolski, Jacek Jakubowski
We present the idea of intertwining of two diffusions by Feynman-Kac operators. We present some variations and implications of the method and give examples of its applications. Amo…
Exact Distribution of Verhulst process
Maciej Wiśniewolski, Jacek Jakubowski
We investigate a Verhulst process, which is the special functional of geometric Brownian motion and has many applications, among others in biology and in stochastic volatility mode…
Risk-minimization and hedging claims on a jump-diffusion market model, Feynman-Kac Theorem and PIDE
Jacek Jakubowski, Mariusz Niewęgłowski
At first, we solve a problem of finding a risk-minimizing hedging strategy on a general market with ratings. Next, we find a solution to this problem on Markovian market with ratin…
Jump-diffusion processes in random environments
Jacek Jakubowski, Mariusz Niewęgłowski
In this paper we investigate jump-diffusion processes in random environments which are given as the weak solutions to SDE's. We formulate conditions ensuring existence and uniquene…
On hyperbolic Bessel processes and beyond
Jacek Jakubowski, Maciej Wiśniewolski
We investigate distributions of hyperbolic Bessel processes. We find links between the hyperbolic cosine of hyperbolic Bessel processes and functionals of geometric Brownian motion…
Intricacies of Dependence between Components of Multivariate Markov Chains: Weak Markov Consistency and Markov Copulae
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Niewęgłowski
This article continues our study of Markovian consistency and Markov copulae. In particular, we characterize the weak Markovian consistency for finite Markov chains. We discuss som…
On some Brownian functionals and their applications to moments in lognormal and Stein stochastic volatility models
Jacek Jakubowski, Maciej Wisniewolski
The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a pro…
Defaultable bonds with an infinite number of Levy factors
Jacek Jakubowski, Mariusz Nieweglowski
A market with defaultable bonds where the bond dynamics is in a Heath-Jarrow-Morton setting and the forward rates are driven by an infinite number of Levy factors is considered. Th…
Linear stochastic volatility models
Jacek Jakubowski, Maciej Wisniewolski
In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of…
On incompleteness of bond markets with infinite number of random factors
Michał Barski, Jacek Jakubowski, Jerzy Zabczyk
The completeness of a bond market model with infinite number of sources of randomness on a finite time interval in the Heath-Jarrow-Morton framework is studied. It is proved that t…