In this paper we consider the problem of determining approximations for distortion risk measures of sums of non-independent random variables. First, we give an overview of the recent actuarial literature on distortion risk measures and convex bounds for sums of random variables. Then, we examine the case 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. The result is then extended to cover the case of non necessarily discrete risks. Finally, the attention is devoted to the analysis of the gap between the risk measures of upper and lower bounds, with the aim of minimizing it.
Bounds for Concave Distortion Risk Measures for Sums of Risks
CAMPANA, Antonella;
2008-01-01
Abstract
In this paper we consider the problem of determining approximations for distortion risk measures of sums of non-independent random variables. First, we give an overview of the recent actuarial literature on distortion risk measures and convex bounds for sums of random variables. Then, we examine the case 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. The result is then extended to cover the case of non necessarily discrete risks. Finally, the attention is devoted to the analysis of the gap between the risk measures of upper and lower bounds, with the aim of minimizing it.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
