Suppose that risk reserves of an insurance company are governed by a Markov-modulated classical risk model with … probability that ruin time, the first time when risk reserve is negative, is finite. We apply Banach contraction principle, q …

This contribution relates to the use of risk measures for determining (re)insurers' economic capital requirements …. Alternative sets of properties of risk measures are discussed. Furthermore, methods for constructing risk measures via … different approaches relate to popular risk measures, such as VaR, Expected Shortfall, distortion risk measures and the …

In this paper, we study two classes of optimal reinsurance models by minimizing the total risk exposure of an insurer … under the criteria of value at risk (VaR) and conditional value at risk (CVaR). We assume that the reinsurance premium is …-continuous retained loss functions, the truncated stop-loss reinsurance is shown to be optimal. In contrast, under CVaR risk measure, the …

Building on a new theory of parametric risk models initiated in Hürlimann(1998), it is shown how mean scaled individual … risk models can be constructed. The approximate computation of their distributions and related quantities can be done in … of models. The method is applied to the construction of a mean scaled operational risk model …

Utility-based shortfall risk (SR) measure proposed by (F\”ollmer and Schied, 2002) has been well studied in risk … problem similar to the definition of SR and subsequently call the premium functional as a generalized shortfall risk measure … preference functional is a distorted expected value function based on prospect theory. Specifically, we exploit Weber's methods …

required is obtained directly from a risk measurement. Using Monte Carlo simulation we show that, in some instances, a common … risk measure such as Value-at-Risk is not subadditive when certain dependence structures are considered. Higher risk …