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  • 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.
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