Value at Risk (VaR) has emerged in recent years as a standard tool to measure and control the risk of trading portfolios. Yet, existing theoretical analyses of the optimal behavior of a trader subject to VaR limits have produced a negative view of VaR as a risk-control tool. In particular, VaR limits have been found to induce increased risk exposure in some states and an increased probability o...

Although controversial from the theoretical point of view, quantile risk measures are widely used by institutions and regulators. In this paper we show that the use of measures like Value at Risk or Conditional Tail Expectation as optimization criteria for insurance or reinsurance leads to treaties that are not enforceable and/or are clearly bad for the cedent. We argue that this is one further...

In this paper it is proved that a concave distortion function is a necessary and sufficient condition for coherence, and a strictly concave distortion function is a necessary and sufficient condition for strict consistency with second order stochastic dominance. The results are related to current risk measures used in practice, such as value-at-risk (VaR) and the conditional tail expectation (C...

Regulatory authorities demand insurance companies to control the risks by imposing stringent risk management policies. This article investigates the insurance company’s optimal risk management strategy subject to regulator’s risk measure constraints. We first design the optimal reinsurance contracts under different tail risk measures. Then we analyze the impact of the regulators’ requirements o...

We explore generalizations of the pari-mutuel model (PMM), a formalization of an intuitive way of assessing an upper probability from a precise one. We discuss a naive extension of the PMM considered in insurance, compare the PMM with a related model, the Total Variation Model, and generalize the natural extension of the PMM introduced by P. Walley and other pertained formulae. The results are ...

The implementation of appropriate statistical techniques for monitoring conditional VaR models, i.e, backtesting, reported by institutions is fundamental to determine their exposure to market risk. Backtesting techniques are important since the severity of the departures of the VaR model from market results determine the penalties imposed for inadequate VaR models. In this paper we make six con...

Recent crises in the financial industry have shown weaknesses in the modeling of Risk-Weighted Assets (RWAs). Relatively minor model changes may lead to substantial changes in the RWA numbers. Similar problems are encountered in the Value-at-Risk (VaR)-aggregation of risks. In this article, we highlight some of the underlying issues, both methodologically, as well as through examples. In partic...

Modeling high-dimensional dependence is widely studied to explore deep relations in multiple variables particularly useful for financial risk assessment. Very often, strong restrictions are applied on a dependence structure by existing high-dimensional dependence models. These restrictions disabled the detection of sophisticated structures such as asymmetry, upper and lower tail dependence betw...

We discuss the CreditRisk+ methodology from the perspective of the moment generating function of the credit factors. This representation lends itself to a new recursion formula for the portfolio loss distribution that is more accurate and considerably faster, particularly for large portfolios. We discuss how the model can be extended to incorporate correlations between risk factors and derive t...