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...

In this paper we investigate the approximations for the distribution function of a sum S of lognormal random variables. These approximations are obtained by considering the conditional expectation E[SΛ] of S with respect to a conditioning random variable Λ.The choice of Λ is crucial in order...