ORCID Identifier(s)

0000-0002-6455-0920

Graduation Semester and Year

2020

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Andrzej Korzeniowski

Abstract

Risk measures emerge in fields such as economics, insurance, finance and are concerned with a stochastic representation of uncertainties stemming from the unpredictability of the real world events. In essence, risk analysis amounts to quantifying the chances of undesirable events and developing a model that limits the impact of potential losses. Assets and liabilities in the Insurance industry, as well as financial goals of Investment companies rely on calculating the probability that their respective portfolios satisfy the preset constraints. On the flip side, risk measures serve both industries by providing optimal strategies for minimizing losses. Our research is concerned with Distorted Risk Measures (DRMs) in stochastic optimization regarding decisions about the size of the risk exposure. We extend the classical Lundberg Risk Model to the case of periodic reinsurance with investment.

Keywords

Lundberg model, Periodic reinsurance with investment, Value-at-Risk, Conditional tail expectation, Distortion risk measures with constraints

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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