Four applications of stochastic processes: Contagious disease, credit risk, gambling and bond portfolios
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
This thesis consists of four papers on applications of stochastic processes.
In Paper I we study an open population SIS (Susceptible - Infective - Susceptible) stochastic epidemic model from the time of introduction of the disease, through a possible outbreak and to extinction. The analysis uses coupling arguments and diffusion approximations.
In Paper II we propose a model describing an economy where companies may default due to contagion. The features of the model are analyzed using diffusion approximations. We show that the model can reproduce oscillations in the default rates similar to what has been observed empirically.
In Paper III we consider the problem of finding an optimal betting strategy for a house-banked casino card game that is played for several coups before reshuffling. A limit result for the return process is found and the optimal card counting strategy is derived. This continuous time strategy is shown to be a natural generalization of the discrete time strategy where the so called effects of removals are replaced by the infinitesimal generator of the card process.
In Paper IV we study interest rate models where the term structure is given by an affine relation and in particular where the driving stochastic processes are so-called generalised Ornstein-Uhlenbeck processes. We show that the return and variance of a portfolio of bonds which are continuously rolled over, also called rolling horizon bonds, can be expressed using the cumulant generating functions of the background driving Lévy processes associated with the OU processes. We also show that if the short rate, in a risk-neutral setting, is given by a linear combination of generalised OU processes, the implied term structure can be expressed in terms of the cumulant generating functions.
Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University , 2011. , 27 p.
Probability Theory and Statistics
Research subject Mathematical Statistics
IdentifiersURN: urn:nbn:se:su:diva-57949ISBN: 978-91-7447-318-6OAI: oai:DiVA.org:su-57949DiVA: diva2:418801
2011-08-26, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
Ethier, Stewart N., Dr.
Nordvall Lagerås, Andreas, Dr.Andersson, Håkan, Dr.
At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Submitted. Paper 3: Submitted. Paper 4: Manuscript.2011-06-062011-05-242011-06-14Bibliographically approved
List of papers