In this paper we examine and summarize properties of several well-known risk measuresthat can be used in the framework of setting solvency capital requirements for a risky business.Special attention is given to the class of (concave) distortion risk measures. We investigatethe relationship...

Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial mathematics...

Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial mathematics...

Modern Actuarial Risk Theory -- Using R contains what every actuary needs to know about non-life insurance mathematics. It starts with the standard material like utility theory, individual and collective model and basic ruin theory. Other topics are risk measures and premium principles,...

This paper illustrates an analytic method that can be used to determine the total capital requirements necessary to properly provide for the future obligations of a portfolio of annuity liabilities and to protect the enterprise from the related risks it faces. This example is based on the work...

We consider a continuous-time Markowitz type portfolio problem that consists of minimizing the discounted cost of a given cash-fl ow under the constraint of a restricted Capital at Risk. In a Black-Scholes setting, upper and lower bounds are obtained by means of simple analytical expressions...