Credibilistic Risk Aversion

In the probabilistic risk aversion approach, risks are presumed as random variables with known probability distributions. However, in some practical cases, for example, due to the absence of historical data, the inherent uncertain characteristic of risks or different subject judgements from the decision makers may be hard or not appropriate to be estimated with probability distributions. Therefore the traditional probabilistic risk aversion theory is ineffective. Thus, in order to deal with these cases, we suggest to measure those kinds of risks as fuzzy variables, and accordingly to present an alternative risk aversion approach by employing the credibility theory. In the present paper, first, the definition of credibilistic risk premium proposed by Georgescu and Kinnunen (2013) is revised by taking the initial wealth into consideration, and provide a general method to compute the credibilistic risk premium. Secondly, regarding the risks represented with the commonly used LR fuzzy intervals, a simple calculation formula for the local credibilistic risk premium is put forward. Finally, in a global sense, several equivalent propositions for the comparative risk aversion under the credibility measurement are provided. Illustrated examples are presented to show the applicability of the theoretical findings