Value at Risk (VaR) is used to illustrate the maximum potential loss under a given confidence level, and is just a single indicator to evaluate risk ignoring any information about income. The present paper will generalize one-dimensional VaR to two-dimensional VaR with income-risk double...

The primary objective of this work is to analyze model based Value-at-Risk associated with mortality risk arising from issued term life assurance contracts and to compare the results with the capital requirements for mortality risk as determined using Solvency II Standard Formula. In particular,...

An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities and the banking/insurance/reinsurance industry. Koch (2017) introduced a notion of spatial risk measure and a corresponding set of axioms which are well suited to analyze the...

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...

This paper provides a critical analysis of the subadditivity axiom, which is the key condition for coherent risk measures. Contrary to the subadditivity assumption, bank mergers can create extra risk. We begin with an analysis how a merger affects depositors, junior or senior bank creditors, and...

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...

In order to protect stakeholders of insurance companies and financial institutions against adverse outcomes of risky businesses, regulators and senior management use capital allocation techniques. For enterprise-wide risk management, it has become important to calculate the contribution of each...

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...

We discuss when and why custom multi-factor risk models are warranted and give source code for computing some risk factors. Pension/mutual funds do not require customization but standardization. However, using standardized risk models in quant trading with much shorter holding horizons is...

The present study aims at modelling market risk for four commodities, namely West Texas Intermediate (WTI) crude oil, natural gas, gold and corn for the period 2007-2017. To this purpose, we use Extreme Value Theory (EVT) together with a set of Conditional Auto-Regressive Logit (CARL) models to...