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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Lévy-Type Processes under Uncertainty and Related Nonlocal Equations

Hollender, Julian 17 October 2016 (has links) (PDF)
The theoretical study of nonlinear expectations is the focus of attention for applications in a variety of different fields — often with the objective to model systems under incomplete information. Especially in mathematical finance, advances in the theory of sublinear expectations (also referred to as coherent risk measures) lay the theoretical foundation for modern approaches to evaluations under the presence of Knightian uncertainty. In this book, we introduce and study a large class of jump-type processes for sublinear expectations, which can be interpreted as Lévy-type processes under uncertainty in their characteristics. Moreover, we establish an existence and uniqueness theory for related nonlinear, nonlocal Hamilton-Jacobi-Bellman equations with non-dominated jump terms.
2

Probability and Heat Kernel Estimates for Lévy(-Type) Processes

Kühn, Franziska 05 December 2016 (has links) (PDF)
In this thesis, we present a new existence result for Lévy-type processes. Lévy-type processes behave locally like a Lévy process, but the Lévy triplet may depend on the current position of the process. They can be characterized by their so-called symbol; this is the analogue of the characteristic exponent in the Lévy case. Using a parametrix construction, we prove the existence of Lévy-type processes with a given symbol under weak regularity assumptions on the regularity of the symbol. Applications range from existence results for stable-like processes and mixed processes to uniqueness results for Lévy-driven stochastic differential equations. Moreover, we discuss sufficient conditions for the existence of moments of Lévy-type processes and derive estimates for fractional moments.
3

Lévy-Type Processes under Uncertainty and Related Nonlocal Equations

Hollender, Julian 12 October 2016 (has links)
The theoretical study of nonlinear expectations is the focus of attention for applications in a variety of different fields — often with the objective to model systems under incomplete information. Especially in mathematical finance, advances in the theory of sublinear expectations (also referred to as coherent risk measures) lay the theoretical foundation for modern approaches to evaluations under the presence of Knightian uncertainty. In this book, we introduce and study a large class of jump-type processes for sublinear expectations, which can be interpreted as Lévy-type processes under uncertainty in their characteristics. Moreover, we establish an existence and uniqueness theory for related nonlinear, nonlocal Hamilton-Jacobi-Bellman equations with non-dominated jump terms.
4

Probability and Heat Kernel Estimates for Lévy(-Type) Processes

Kühn, Franziska 25 November 2016 (has links)
In this thesis, we present a new existence result for Lévy-type processes. Lévy-type processes behave locally like a Lévy process, but the Lévy triplet may depend on the current position of the process. They can be characterized by their so-called symbol; this is the analogue of the characteristic exponent in the Lévy case. Using a parametrix construction, we prove the existence of Lévy-type processes with a given symbol under weak regularity assumptions on the regularity of the symbol. Applications range from existence results for stable-like processes and mixed processes to uniqueness results for Lévy-driven stochastic differential equations. Moreover, we discuss sufficient conditions for the existence of moments of Lévy-type processes and derive estimates for fractional moments.

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