Quantitative risk assessment, aggregation functions and capital allocation problems
This work is focused on the study of risk measures and solutions to capital allocation problems, their suitability to answer practical questions in the framework of insurance and financial institutions and their connection with a family of functions named aggregation operators. These operators are we...
| Autor: | |
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| Formato: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | España |
| Recursos: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/319687 |
| Acesso em linha: | http://hdl.handle.net/10803/319687 |
| Access Level: | acceso abierto |
| Palavra-chave: | Risc (Economia) Riesgo (Economía) Risk Capital Econometria Econometría Econometrics Ciències Jurídiques, Econòmiques i Socials 33 |
| Resumo: | This work is focused on the study of risk measures and solutions to capital allocation problems, their suitability to answer practical questions in the framework of insurance and financial institutions and their connection with a family of functions named aggregation operators. These operators are well-known among researchers from the information sciences or fuzzy sets and systems community. The first contribution of this dissertation is the introduction of GlueVaR risk measures, a family belonging to the more general class of distortion risk measures. GlueVaR risk measures are simple to understand for risk managers in the financial and insurance sectors, because they are based on the most popular risk measures (VaR and TVaR) in both industries. For the same reason, they are almost as easy to compute as those common risk measures and, moreover, GlueVaR risk measures allow to capture more intricated managerial and regulatory attitudes towards risk. The definition of the tail-subadditivity property for a pair of risks may be considered the second contribution. A distortion risk measure which satisfies this property has the ability to be subadditive in extremely adverse scenarios. In order to decide if a GlueVaR risk measure is a candidate to satisfy the tail-subadditivity property, conditions on its parameters are determined. It is shown that distortion risk measures and several ordered weighted averaging operators in the discrete finite case are mathematically linked by means of the Choquet integral. It is shown that the overall aggregation preference of the expert may be measured by means of the local degree of orness of the distortion risk measure, which is a concept taken over from the information sciences community and brung into the quantitative risk management one. New indicators for helping to characterize the discrete Choquet integral are also presented in this dissertation. The aim is complementing those already available, in order to be able to highlight particular features of this kind of aggregation function. Following this spirit, the degree of balance, the divergence, the variance indicator and Rényi entropies as indicators within the framework of the Choquet integral are here introduced. A major contribution derived from the relationship between distortion risk measures and aggregation operators is the characterization of the risk attitude implicit into the choice of a distortion risk measure and a confidence or tolerance level. It is pointed out that the risk attitude implicit in a distortion risk measure is to some extent contained in its distortion function. In order to describe some relevant features of the distortion function, the degree of orness indicator and a quotient function are used. It is shown that these mathematical devices give insights on the implicit risk behavior involved in risk measures and entail the definitions of overall, absolute and specific risk attitudes. Regarding capital allocation problems, a list of key elements to delimit these problems is provided and mainly two contributions are made. Firstly, it is shown that GlueVaR risk measures are as useful as other alternatives like VaR or TVaR to solve capital allocation problems. The second contribution is understanding capital allocation principles as compositional data. This interpretation of capital allocation principles allows the connection between aggregation operators and capital allocation problems, with an immediate practical application: Properly averaging several available solutions to the same capital allocation problem. This thesis contains some preliminary ideas on this connection, but it seems to be a promising research field. |
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