In this paper, we develop a framework for measuring, allocating and managing systemic risk. SystRisk, our measure of total systemic risk, captures the a priori cost to society for providing tail-risk insurance to the financial system. Our allocation principle distributes the total systemic risk...

Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult task. In this paper, we demonstrate how this can be successfully accomplished when losses follow the multivariate Pareto distribution of the second kind, which is an attractive...

This paper proposes risk sharing strategies, which allow insurers to cooperate and diversify non-systemic risk. We deal with both deviation measures and coherent risk measures and provide general mathematical methods applying to optimize them all. Numerical examples are given in order to...

This paper uses mortality fan charts to illustrate prospective future male mortality. These fan charts show both the most likely path of male mortality and the bands of uncertainty surrounding that path. The fan charts are based on a model of male mortality that is known to provide a good fit to...

It is well known that a random vector with given marginals is comonotonic if and only if it has the largest convex sum, and that a random vector with given marginals (under an additional condition) is mutually exclusive if and only if it has the minimal convex sum. This paper provides an...

This paper proposes a new method to introduce coherent risk measures for risks with infinite expectation, such as those characterized by some Pareto distributions. Extensions of the conditional value at risk, the weighted conditional value at risk and other examples are given. Actuarial...

A spectrum of upper bounds (Qα(X ; p) ae[0,∞] on the (largest) (1-p)-quantile Q(X;p) of an arbitrary random variable X is introduced and shown to be stable and monotonic in α, p, and X , with Q0(X ;p) = Q(X;p). If p is small enough and the distribution of X is regular enough, then Qα(X ; p)...

Since late 2019, during one of the largest pandemics in history, COVID-19, global economic recession has continued. Therefore, investors seek an alternative investment that generates profits during this financially risky situation. Cryptocurrency, such as Bitcoin, has become a new currency tool...

In this paper, the generalized Pareto distribution (GPD) copula approach is utilized to solve the conditional value-at-risk (CVaR) portfolio problem. Particularly, this approach used (i) copula to model the complete linear and non-linear correlation dependence structure, (ii) Pareto tails to...

This paper investigates the risk exposure for options and proposes MaxVaR as an alternative risk measure which captures the risk better than Value-at-Risk especially. While VaR is a measure of end-of-horizon risk, MaxVaR captures the interim risk exposure of a position or a portfolio. MaxVaR is...