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, risks 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 measuring these kinds of risks as fuzzy variables, and accordingly to present an alternative risk aversion approach by employing credibility theory. In the present paper, first, the definition of credibilistic risk premium proposed by Georgescu and Kinnunen [Fuzzy Inf. Eng., 2013, 5, 399-416] is revised by taking the initial wealth into consideration, and then a general method to compute the credibilistic risk premium is provided. Secondly, regarding the risks represented with the commonly used LR fuzzy intervals, a simple calculation formula of the local credibilistic risk premium is put forward. Finally, in a global sense, several equivalent propositions for comparative risk aversion under the credibility measurement are provided. Illustrated examples are presented to show the applicability of the theoretical findings.