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...

In an actuarial or financial context one often encounters the calculation of risk measures of random variables of the type S r:1 Xi' In many applications, the individual risks Xi are not mutually independent, for example because their outcomes are all influenced by the same economic or physical...

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...