5 documents found

Master thesis
CC BY 4.0
2020

The 1-2-random walk : some bijections and a central limit theorem

A deeply researched topic in stochastic is the random walk. The most basic concept considers being at the starting point 0, and going 1 into positive or negative range with 50% probability each. Many problems have been solved for this stochastic process, for example the probability of returning to 0...
Dissertation
All rights reserved
2020

Solutions to the SEP and position control problems using FBSDEs and simulation...

We solve the Skorokhod embedding problem for a class of stochastic processes satisfying an inhomogeneous stochastic differential equation (SDE) of the form At = µ(t,At)dt + σ(t,At)dWt. We provide sufficient conditions guaranteeing that for a given probability measure ν on the real numbers there exists...
Master thesis
CC BY 4.0
2020

Risikoneutrale Bewertung unter rauer Volatilität

Historische und aktuelle Marktdaten lassen darauf schließen, dass die klassische Annahme einer konstanten Volatilität für die meisten Assets zu stark vereinfachend ist. Stattdessen scheint auch die Volatilität selbst ein stochastischer Prozess zu sein. Im Rahmen dieser Arbeit wird anhand von zwei Datensätzen...
Master thesis
All rights reserved
2019-04-04

The maximum principle and controlled diffusion

The objective of this master thesis is to solve a controlled diffusion problem via Pontryagin's maximum principle. To that end, we review in the first part basic notions that are relevant for the course of this thesis. In the second part, we study a controlled diffusion problem, in which one completely...
Dissertation
CC BY 3.0
2018

Optimal stopping problems with expectation constraints

In this thesis we investigate optimal stopping problems with expectation cost constraints. We focus on reducing the set of stopping times as well as on deriving a partial differential equation for the value function. If the process to stop is a time-homogeneous Ito-process, we show, by introducing a...