TY  - THES
AB  - This thesis is devoted to the study of risk-sensitive stochastic control and large deviations of a certain class of affine stochastic models. These are processes with an exponential-affine form of their characteristic function.  The work is structured into two main parts. In the first part, we consider subcritical continuous-state branching processes with immigration (CBI processes), which are a special case of affine processes. Specifically, we investigate limit theorems for the time-averaged process\begin{displaymath}    \left( \frac{1}{t} \int_0^t X_s^x ds\right)_{t\ge 0},\end{displaymath}where $X^x$ is the subcritical CBI process with initial condition $x\ge 0$. In particular, we establish a large deviation principle (LDP) under the assumption that the branching and immigration Lévy measures associated with the CBI process $X^x$ have finite exponential moments for big jumps. Furthermore, we provide a semi-explicit expression for the corresponding good rate function, associated with the LDP, in terms of the branching and immigration mechanisms characterizing the CBI process $X^x$. In the second part of the thesis, we study a risk-sensitive asset management (RSAM) stochastic optimal control problem. Specifically, we consider the RSAM problem of finding an optimal investment strategy $h$ for a risk-averse investor over a finite time horizon. This investor is assumed to reside in a financial market driven by an $\alpha$-CIR factor model, an affine process that extends the standard Cox–Ingersoll–Ross (CIR) model by incorporating a jump part driven by $\alpha$-stable Lévy processes with index $\alpha \in (1,2)$. We obtain a semi-explicit representation of the optimal investment strategy maximizing the wealth of the investor, and we prove its optimality.
AU  - Abdellatif, Mariem
CY  - Wuppertal
DO  - 10.25926/BUW/0-986
DP  - Bergische Universität Wuppertal
KW  - Stochastic processes
KW  - CBI processes
KW  - Large deviation principle (LDP)
KW  - Stochastic control
KW  - Risk-sensitive stochastic control
LA  - ger
N1  - Bergische Universität Wuppertal, Dissertation, 2025
PB  - Veröffentlichungen der Universität
PY  - 2025
SP  - 1 Online-Ressource (ix, 87 Seiten) : Illustrationen
T2  - Mathematik und Informatik
TI  - Control and large deviations of some affine stochastic models
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:468-2-6720
Y2  - 2026-03-27T15:11:24
ER  -