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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 41020 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Alishahi, Kasra
- Abstract:
- This thesis is devoted to introduce coherent risk measures on general probability spaces. After studying their properties, we also will characterize them using functional analysis tools. First we describe some related economic concepts such as risk concept, risk management and risk measures. Then we will study Value at Risk (VaR) as an applicable risk measure and determine its advantages and disadvantages. The motivation for studying risk measures in an axiomatic point of view and also introducing coherent risk measures was that VaR doesn’t have the diversification property. In chapter 2 and 3, we introduced coherent risk measures comprehensively. We began the second chapter by the mathematical definition of these measures and also mentioning some of their properties like their relation to VaR. The last part of the second chapter is contained by characterization of coherent risk measures using Bipolar theorem. In chapter3, these measures have been extended into the general probability spaces. The application of coherent risk measures in fair capital allocation problem for covering risk is the subject of chapter 4. It also includes the definition of comonotone coherent risk measures and the characterization of them using convex game theory literature
- Keywords:
- Risk Management ; Risk Measure ; Value at Risk ; Coherent Risk Measure ; Capital Allocation Problem
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