Lévy-Type Processes under Uncertainty and Related Nonlocal Equations

Julian Hollender

AutorIn

Julian Hollender

Titel

Lévy-Type Processes under Uncertainty and Related Nonlocal Equations

Zitierfähige Url:

https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa-211795

Datum der Einreichung

13.07.2016

Datum der Verteidigung

12.10.2016

ISBN

1535553847

Abstract (EN)

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.

Freie Schlagwörter (DE)

Wahrscheinlichkeitstheorie, Analysis, Stochastische Analysis, Stochastische Prozesse, Risikomaße, Finanzmathematik, Risikomaße, Sublineare Erwartungswerte, Nichtlineare Erwartungswerte, Lévy-typ Prozesse, Nichtlokale Gleichungen, HJB Gleichungen, Knightian Uncertainty

Freie Schlagwörter (EN)

Probability Theory, Analysis, Stochastic Analysis, Stochastic Processes, Risk Measures, Mathematical Finance, Risk Measures, Sublinear Expectation, Nonlinear Expectation, Lévy-Type Processes, Nonlocal Equations, HJB Equations, Knightian Uncertainty

Klassifikation (DDC)

510

Klassifikation (RVK)

SK 820, SK 980

GutachterIn