In this paper we consider the problem of studying the gap between bounds of risk measures of sums of non-independent random variables. Owing to the choice of the context where to set the problem, namely that of distortion risk measures, we first deduce an explicit formula for the risk measure of a discrete risk by referring to its writing as sum of layers. Then, we examine the case of sums of discrete risks with identical distribution. Upper and lower bounds for risk measures of sums of risks are presented in the case of concave distortion functions. Finally, the attention is devoted to the analysis of the gap between risk measures of upper and lower bounds, with the aim of optimizing it.
|Data di pubblicazione:||2008|
|Titolo:||Bounds for Concave Distortion Risk Measures for Sums of Risks|
|Titolo del libro:||Mathematical and Statistical Methods in Insurance and Finance|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/978-88-470-0704-8_6|
|Appare nelle tipologie:||3.1 Articolo su libro|
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