A study on dependence functions and risk measures.

Author(s)

Marcelo Gonçalves

• Document type: Doctoral Thesis
• Press: São Paulo. , ilustrações, tabelas.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2008-11-28

Examining board members

Nikolai Valtchev Kolev; Cristiano Augusto Coelho Fernandes; Veronica Andrea Gonzalez Lopez; Pedro Alberto Morettin

• Advisor: Nikolai Valtchev Kolev; Antonio Elias Fabris
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics
• Indexed in: Banco de Dados Bibliográficos da USP-DEDALUS; Biblioteca Digital de Teses e Dissertações - USP
• Location: Universidade de São Paulo. Instituto de Matemática e Estatística. Biblioteca Carlos Benjamin de Lyra; QA282.42.4.T e.2; G635e

Abstract

We begin our work studying an special class of quantile risk measures, known as distorted risk measures. The basic assumption is that the risk manager does not know the complete dependence structure (that is, the risks\'s joint distribution) embedded in the risk\'s portfolio, what makes the exact computation of the risk measure an impossible task. This is a common scenario in practical problems. We present two approaches to compute bounds for the distorted risk measures in such situation, underlining the pros and cons of each one. In risk modeling, in the absence of complete knowledge regarding their joint distribution, one often relies on the copula function approach. However, copulas have been criticized in recent publications mostly because it ignores the marginal behavior and smash the data into the unity square. In order to overcome such problems we present and alternative and complement to the copula approach: the Sibuya dependence function. (AU)