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oai:elekpub.bib.uni-wuppertal.de:82566122026-03-24T12:00:06ZubwhsoaDoctoralThesis

vls/2603noah-balancer_mdapi1elekpub.bib.uni-wuppertal.devdControl and large deviations of some affine stochastic modelsAbdellatif, MariemVerfasserautRüdiger, BarbaraAkademischer BetreuerdgsTrabelsi, ChirazAkademischer BetreuerdgsKassing, SebastianAkademischer BetreuerdgsKruze, ThomasAkademischer BetreuerdgsBergische Universität WuppertalGrad-verleihende InstitutiondggtextthesisTextHochschulschriftthesisdoctoralThesisgwXA-DEWuppertal2025single unitgerelectronic resourceremotetext/htmltext/html1 Online-Ressource (ix, 87 Seiten) : IllustrationenComputerOnline-RessourceThis 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.vorgelegt von Mariem AbdellatifBergische Universität Wuppertal, Dissertation, 2025Stochastic processesCBI processesLarge deviation principle (LDP)Stochastic controlRisk-sensitive stochastic controlWuppertal510519urn:nbn:de:hbz:468-2-672010.25926/BUW/0-98699376766414106441Druck-AusgabeHT031436397https://dx.doi.org/10.25926/BUW/0-986https://nbn-resolving.org/urn:nbn:de:hbz:468-2-6720Open AccessCC BY 4.02025-12-18oaDoctoralThesispublicrda26031920260602105636.0CT009000486s2w-hsswupubwgerUBW:C:C.01 https://elekpub.bib.uni-wuppertal.de//domainresource/static/graphics/connectors/viewerLogo.gifWuppertal : Bergische Universität Wuppertalcc-by https://ub-wuppertal.digibib.net/search/katalog/record/(DE-605)urn%3Anbn%3Ade%3Ahbz%3A468-2-6720 https://elekpub.bib.uni-wuppertal.de/id/8256612 https://elekpub.bib.uni-wuppertal.de/i3f/v20/8256612/manifest https://elekpub.bib.uni-wuppertal.de/proto_ftsearch/8256612