Credible risk measures with applications in actuarial sciences and finance

In this paper, we introduce a general framework for obtaining a new type of risk measures, the so called credible risk measures, as a result of incorporating credibility methodology with some well known risk measures, such as the value at risk (VaR) and the conditional tail expectation (CTE). The resulting credible risk measures are more informative than the usual risk measures (i.e. VaR, CTE) in capturing the risk of individual insurer's contract (or returns of an individual asset) as well as the portfolio risk consisting of several similar but not identical contracts (or returns of a portfolio of similar assets), which are grouped together to share the risk. These credible risk measures are: the credible value at risk, the credible conditional tail expectation, the credible tail conditional median and the credible quantile tail expectation. Two examples of credible risks measures are presented, one with insurance loss data and the other with industry financial data. The advantages and disadvantages of these new credible measures are also discussed.