In the presentation we propose a method which generates parameters (interest rate, transition intensities, etc.), drawn from a given set, that maximize the reserve. We will refer to this as generating an endogenous (with respect to the model used to calculate the reserves) stress scenario. These endogenous stress scenarios can be used in e.g. calculation of solvency capital requirements or in risk management in general. Focus of the presentation is on computational aspects.

Finding the parameters that maximize the reserve is a common actuarial practice. In the new solvency regime of the European Union (Solvency II) this is done in form of a Value-at-Risk (VaR) approach and used in order to calculate the Solvency Capital Requirement (SCR). We propose an endogenous stress scenario which can be chosen such that the resulting capital requirement is on the safe side (higher) of VaR. Finally, for risk management in general the endogenous stress scenario is relevant for premium settlement of traditional with-profits life insurance products making sure that the resulting premiums are high enough to cover the benefits in essentially all realistic scenarios.

When the biometrical intensities vary independently, the endogenous stress scenario can be found as in Christiansen, M.C. (2010). However, in the presentation we allow for dependence which is in accordance with the Solvency II framework. First between the transition intensities and, second between transition intensities and the interest rate, where interest rate dependent surrender intensity is a relevant example. In general, finding the endogenous stress scenario is equivalent to solving partial differential equations. However, there are some important situations where this can be reduced to systems of ordinary differential equations resembling those solved when computing the traditional reserve. In the presentation we take concrete examples and show the formalistic results as well as numerical illustrations of our main points.

In addition to Mr. Schomaker, the authors of this report are:

• Marcus C. Christiansen, University of Ulm

• Lars Frederik Brandt Henriksen, University of Copenhagen

• Mogens Steffensen. University of Copenhagen

References:

• Christiansen, M.C. (2010). Biometric worst-case scenarios for multi-state life insurance policies. Insurance: Mathematics and Economics 47, 190-197.