Operational Risk and Insurance: A Ruin-probabilistic Reserving Approach

A new methodology for financial and insurance operational risk capital estimation is proposed. It is based on using the finite time probability of (non)ruin as an operational risk measure, under a general ruin probability model, according to which operational losses may have any joint (dependent) discrete or continuous distribution, and the function, describing the accumulation of risk capital may be any nondecreasing, positive real function hHtL . The probability of nonruin is explicitly expressed using closed form expressions, derived by Ignatov and Kaishev (2000, 2004) and Ignatov Kaishev and Krachunov (2001) and by setting it to a high enough preassigned value, say 0.99, it is possible to obtain not just a value for the capital charge but a (dynamic) risk capital accumulation strategy hHtL . In view of its generality, the proposed methodology is capable of accommodating any (heavy tailed) distributions, such as the Generalized Pareto Distribution, the Lognormal distribution the g-and-h distribution and the GB2 distribution. Applying our methodology on numerical examples, we demonstrate that dependence in the loss severities may have a dramatic effect on the estimated risk capital. In addition we also show that one and the same high enough survival probability may be achieved by different risk capital accumulation strategies one of which may possibly be preferable to accumulating capital just linearly, as has been assumed by Embrechts et al. (2004). The proposed methodology takes into account also the effect of insurance on operational losses, in which case it is proposed to take the probability of joint survival of the financial institution and the insurance provider as a joint operational risk measure. The risk capital allocation strategy is then obtained in such a way that the probability of joint survival is equal to a preassigned high enough value, say 99.9 %.