53 citations · 134 across the 31 of their papers we have counts for
37 papers
Continuous-Time Reinforcement Learning for Controlled Hawkes Jump-Diffusions
Tomasz R. Bielecki, Thibaut Mastrolia, Haoze Yan
We study stochastic control of multivariate Hawkes-driven stochastic differential equations with machine learning algorithms in a non-Markovian setting. Due to the path dependence…
Robo-Advising in Motion: A Model Predictive Control Approach
Tomasz R. Bielecki, Igor Cialenco
Robo-advisors (RAs) are automated portfolio management systems that complement traditional financial advisors by offering lower fees and smaller initial investment requirements. Wh…
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…
Time consistency of dynamic risk measures and dynamic performance measures generated by distortion functions
Tomasz R. Bielecki, Igor Cialenco, Hao Liu
The aim of this work is to study risk measures generated by distortion functions in a dynamic discrete time setup, and to investigate the corresponding dynamic coherent acceptabili…
The two-sided exit problem for an additive functional of a time-inhomogeneous Markov chain
Tomasz R. Bielecki, Ziteng Cheng, Ruoting Gong
We consider an additive functional driven by a time-inhomogeneous Markov chain with a finite state space. Our study focuses on the joint distribution of the two-sided exit time and…
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…
Risk Filtering and Risk-Averse Control of Markovian Systems Subject to Model Uncertainty
Tomasz R. Bielecki, Igor Cialenco, Andrzej Ruszczyński
We consider a Markov decision process subject to model uncertainty in a Bayesian framework, where we assume that the state process is observed but its law is unknown to the observe…
Risk-sensitive Markov decision problems under model uncertainty: finite time horizon case
Tomasz R. Bielecki, Tao Chen, Igor Cialenco
In this paper we study a class of risk-sensitive Markovian control problems in discrete time subject to model uncertainty. We consider a risk-sensitive discounted cost criterion wi…
Wiener-Hopf Factorization for Arithmetic Brownian Motion with Time-Dependent Drift and Volatility
Tomasz R. Bielecki, Ziteng Cheng, Ruoting Gong
In this paper we obtain a Wiener-Hopf type factorization for a real-valued arithmetic Brownian motion with time-dependent drift and volatility. To the best of our knowledge, this p…
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…
Time-inconsistent Markovian control problems under model uncertainty with application to the mean-variance portfolio selection
Tomasz R. Bielecki, Tao Chen, Igor Cialenco
In this paper we study a class of time-inconsistent terminal Markovian control problems in discrete time subject to model uncertainty. We combine the concept of the sub-game perfec…
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…
Fair Estimation of Capital Risk Allocation
Tomasz R. Bielecki, Igor Cialenco, Marcin Pitera +1
In this paper we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but trac…
A Dynamic Model of Central Counterparty Risk
Tomasz R. Bielecki, Igor Cialenco, Shibi Feng
We introduce a dynamic model of the default waterfall of derivatives CCPs and propose a risk sensitive method for sizing the initial margin (IM), and the default fund (DF) and its…
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…
Adaptive Robust Control Under Model Uncertainty
Tomasz R. Bielecki, Tao Chen, Igor Cialenco +2
In this paper we propose a new methodology for solving an uncertain stochastic Markovian control problem in discrete time. We call the proposed methodology the adaptive robust cont…
Arbitrage-Free Pricing Of Derivatives In Nonlinear Market Models
Tomasz R. Bielecki, Igor Cialenco, Marek Rutkowski
The objective of this paper is to provide a comprehensive study no-arbitrage pricing of financial derivatives in the presence of funding costs, the counterparty credit risk and mar…
Recursive Construction of Confidence Regions
Tomasz R. Bielecki, Tao Chen, Igor Cialenco
Assuming that one-step transition kernel of a discrete time, time-homogenous Markov chain model is parameterized by a parameter , we derive a recursive (in time…
A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective
Tomasz R. Bielecki, Igor Cialenco, Marcin Pitera
In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures, focusing on a the discrete time setup. The two key operatio…
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…
Dynamic Conic Finance via Backward Stochastic Difference Equations
Tomasz R. Bielecki, Igor Cialenco, Tao Chen
We present an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities in a discrete time setup using theory of dynamic acceptability indi…