measures of risk. Furthermore, Qα(X ; p) is the optimal value in a certain minimization problem, the minimizers in which are … problems. In finance, Q0(X;p) and Q1(X ; p) are known as the value at risk (VaR) and the conditional value at risk (CVaR). The … sensitivity to risk. The problems of the effective computation of the bounds are considered. Various other related results are …

The computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed … produce closed-form approximation of the risk measures for variable annuity guaranteed benefits. The techniques are further … developed in this paper to address in a systematic way risk measures for death benefits with the consideration of dynamic …