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David Criens

Other affiliations: University of Freiburg
Bio: David Criens is an academic researcher from Technische Universität München. The author has contributed to research in topics: Martingale (probability theory) & Mathematics. The author has an hindex of 5, co-authored 42 publications receiving 103 citations. Previous affiliations of David Criens include University of Freiburg.

Papers published on a yearly basis

Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors derived equivalent conditions for the (local) absolute continuity of two laws of semimartingales on random sets, which is based on a generalized Girsanov's theorem.
Abstract: We derive equivalent conditions for the (local) absolute continuity of two laws of semimartingales on random sets. Our result generalizes previous results for classical semimartingales by replacing a strong uniqueness assumption by a weaker uniqueness assumption. The main tool is a generalized Girsanov’s theorem, which relates laws of two possibly explosive semimartingales to a candidate density process. Its proof is based on an extension theorem for consistent families of probability measures. Moreover, we show that in a one-dimensional Ito-diffusion setting our result reproduces the known deterministic characterizations for (local) absolute continuity. Finally, we give a Khasminskii-type test for the absolute continuity of multidimensional Ito-diffusions and derive linear growth conditions for the martingale property of stochastic exponentials.

10 citations

Journal ArticleDOI
TL;DR: In this article, the authors derive deterministic criteria for the existence and nonexistence of equivalent martingale measures for financial markets driven by multi-dimensional time-inhomogeneous diffusions.
Abstract: We derive deterministic criteria for the existence and nonexistence of equivalent (local) martingale measures for financial markets driven by multi-dimensional time-inhomogeneous diffusions. Our conditions can be used to construct financial markets in which the no unbounded profit with bounded risk condition holds, while the classical no free lunch with vanishing risk condition fails.

9 citations

Journal ArticleDOI
TL;DR: In this paper, the authors prove limit theorems for cylindrical martingale problems associated with Levy generators and give sufficient and necessary conditions for the Feller property of well-posed problems with continuous coefficients.
Abstract: We prove limit theorems for cylindrical martingale problems associated with Levy generators. Furthermore, we give sufficient and necessary conditions for the Feller property of well-posed problems with continuous coefficients. We discuss two applications. First, we derive continuity and linear growth conditions for the existence of weak solutions to infinite-dimensional stochastic differential equations driven by Levy noise. Second, we derive continuity, local boundedness and linear growth conditions for limit theorems and the Feller property of weak solutions to stochastic partial differential equations driven by Wiener noise.

8 citations

Posted Content
TL;DR: In this article, the authors derive integral tests for the existence and absence of arbitrage in a financial market with one risky asset which is either modeled as stochastic exponential of an Ito process or a positive diffusion with Markov switching.
Abstract: We derive integral tests for the existence and absence of arbitrage in a financial market with one risky asset which is either modeled as stochastic exponential of an Ito process or a positive diffusion with Markov switching. In particular, we derive conditions for the existence of the minimal martingale measure. We also show that for Markov switching models the minimal martingale measure preserves the independence of the noise and we study how the minimal martingale measure can be modified to change the structure of the switching mechanism. Our main mathematical tools are new criteria for the martingale and strict local martingale property of certain stochastic exponentials.

8 citations

Posted Content
TL;DR: In this article, the authors studied monotone and convex stochastic orders for processes with independent increments and derived explicit conditions on the characteristics of the processes via constructions of couplings.
Abstract: We study monotone and convex stochastic orders for processes with independent increments. Our contributions are twofold: First, we relate stochastic orders of the Poisson component to orders of their (generalized) Levy measures. The relation is proven using an interpolation formula for infinitely divisible laws. Second, we derive explicit conditions on the characteristics of the processes. In this case, we prove the conditions via constructions of couplings.

7 citations


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Book
01 Jan 2013
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
Abstract: Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

1,957 citations

Book ChapterDOI
31 Oct 2006

1,424 citations

01 Jan 2016

420 citations

Journal Article
01 Jan 1993-Metrika
TL;DR: In this paper, the existence and uniqueness of Q-functions are discussed. But they focus on transition functions and do not address the uniqueness problem in the context of transition functions.
Abstract: Contents: Transition Functions and Resolvents.- Existence and Uniqueness of Q-Functions.- Examples of Continuous Time Markov Chains.- More on the Uniqueness Problem.- Classification of States and Invariant Measures.- Strong and Exponential Ergodicity.- Reversibility, Monotonictity, and Other Properties.- Birth and Death Processes.- Population Processes.- Bibliography.- Symbol Index.- Author Index.- Subject Index.

348 citations