Pure and Applied Mathematics
http://repository.aust.edu.ng/xmlui/handle/123456789/442
This collection contains Masters Theses of Pure and Applied Mathematics from 2009 to 2019.2021-12-02T20:14:21ZLoss Function in Acturial Science and Estimation
http://repository.aust.edu.ng/xmlui/handle/123456789/4953
Loss Function in Acturial Science and Estimation
Zulaihat, Hassan
The non-life insurance pricing consists of establishing a premium or a tariff paid by the insured to the insurance company in exchange for the risk transfer. A key factor in doing that is properly estimating the distribution that the claim and frequency of claim follows.
This thesis aim at having a deep knowledge of loss function and their estimation, several concept from Measure Theory, Probability Theory and Statistics were combined in the study of loss function and estimating them is illustrated using insurance data set distributed by the Data Sciences website https://www.kaggle.com. The software R is used to obtained our results.
2019-06-23T00:00:00ZIntegration in Lattice Spaces
http://repository.aust.edu.ng/xmlui/handle/123456789/4952
Integration in Lattice Spaces
Doumbia, Fatima
The goal of this thesis is to extend the notion of integration with respect to a measure to Lattice spaces. To do so the paper is first summarizing the notion of integration with respect to a measure on R. Then, a construction of an integral on Banach spaces called the Bochner integral is introduced and the main focus which is integration on lattice spaces is lastly addressed.
2019-06-22T00:00:00ZFoundation of Stochastic Modeling and Applications
http://repository.aust.edu.ng/xmlui/handle/123456789/4951
Foundation of Stochastic Modeling and Applications
Sani, Rahama Abdullahi
This thesis presents an overview on the theory of stopping times, martingales and Brownian motion which are the foundations of stochastic modeling. We started with a detailed study of discrete stopping times and their properties. Next, we reviewed the theory of martingales and saw an application to solving the problem of "extinction of populations". After that, we studied stopping times in the continuous case and finally, we treated extensively the concepts of Brownian motion and the Wienner integral.
2019-06-22T00:00:00ZVariational Inequality in Hilbert Spaces and their Applications
http://repository.aust.edu.ng/xmlui/handle/123456789/4949
Variational Inequality in Hilbert Spaces and their Applications
Udeani, Cyril Izuchukwu
The study of variational inequalities frequently deals with a mapping F from a vector 0 space X or a convex subset of X into its dual X . Let H be a real Hilbert space and a(u, v) be a real bilinear form on H. Assume that the linear and continuous 0 mapping A : H −→ H determines a bilinear form via the pairing a(u, v) = hAu, vi.0 Given K ⊂ H and f ∈ H . Then, Variational inequality(VI) is the problem of finding u ∈ K such that a(u, v − u) ≥ hf, v − ui, for all v ∈ K. In this work, we outline some results in theory of variational inequalities. Their relationships with other problems of Nonlinear Analysis and some applications are also discussed.
2019-06-23T00:00:00Z