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Control and large deviations of some affine stochastic models
C Additional preliminaries
1 Introduction
1.1 Basic Notation
1.2 Structure of the thesis
2 A large deviations principle for time averages of continuous-state branching processes with immigration
2.1 Affine processes
2.2 Stochastic representation of CBI processes
2.3 Moments of the CBI process
2.4 Long-term asymptotics of the time-averaged subcritical CBI-process
2.4.1 Law of large numbers in as L²
2.4.2 Central limit theorem
2.4.3 Large deviation principle
3 Risk-Sensitive Asset Management under an α-CIR Factor Model
3.1 Market model with α-CIR Factor
3.2 Risk-Sensitive Asset Management (RSAM)
3.3 Formal derivation of the HJB equation for the RSAM problem
3.3.1 Stochastic Control
3.3.2 Deriving the Hamilton–Jacobi–Bellman (HJB) equation
3.4 Existence of a classical C1,2 solution
3.5 Verification Theorem
A Large deviation Principle
B Affine processes
C Additional preliminaries
Bibliography
Dissertation
Control and large deviations of some affine stochastic models / vorgelegt von Mariem Abdellatif
Entstehung
Wuppertal
2025
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