Thesis supervisor: Mátyás Barczy
Location of studies (in Hungarian): Debreceni Egyetem Informatikai Kar Abbreviation of location of studies: DE IK
Description of the research topic:
Affine processes and more generally polynomial processes are common generalizations of continuous time and continuous state branching processes with immigration and
so-called Ornstein-Uhlenbeck type processes. Roughly speaking, the affine property means that the logarithm of the characteristic function of the process in question at any time is exponentially affine with respect to the initial state. These processes have been frequently applied in financial mathematics since they can be well-fitted to financial time series, and also due to their computational tractability. One of the aims of a doctoral thesis could be studying of representations of affine and polynomial processes as pathwise unique strong solutions of some appropriate stochastic differential equation, studying existence of a unique stationary distribution and the question of ergodicity. Another aim could be deriving maximum likelihood and conditional least squares estimators of some parameters of these processes based on continuous time and discrete time observations, and studying asymptotic properties of these estimators, respectively.
Bibliography
1. Duffie, D., Filipović, D. and Schachermayer, W.:
Affine processes and applications in finance.
Annals of Applied Probability 13 984-1053, (2003).
2. Meyn, Sean P. and Tweedie, R. L.: Stability of
Markovian processes III: Foster-Lyapunov criteria for continuous-time processes. Advances in Applied
Probability 25 518-548, (1993).
3. Ben Alaya, M. and Kebaier, M.: Parameter estimation for the square root diffusions: ergodic and nonergodic cases. Stochastic Models 28 609-634, (2012).
4. Cuchiero, C., Keller-Ressel, M., Teichmann, J.: Polynomial processes and their applications to mathematical finance, Finance and Stochastics 16 711-740, (2012).
Recommended language skills (in Hungarian): angol Number of students who can be accepted: 1
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