In this paper, we study the worst-case distortion risk measure when information about distortion functions is partially available. We obtain the explicit forms of the worst-case distortion functions from several different sets of plausible distortion functions. When there is no concavity...

This paper considers the financial optimization problem of a firm with several sub-businesses striving for its optimal RORAC. An insightful example shows that the implementation of classical gradient capital allocation can be suboptimal if division managers are allowed to venture into all...

We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding adjusted Expected Shortfalls quantify risk as the minimum...

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...

We develop a normative framework for the optimal design, value assessment, and risk management integration of combined custom contingent claims. A risk averse firm faces a mix of financially insurable and noninsurable risk. The firm seeks optimal positioning in a pair of custom claims, one...

In previous works, the importance of risk management implementation was addressed with regard to the problem of bankruptcy threat, with the explanation of risk impact on higher bankruptcy costs or the underinvestment problem. However, the evaluation of the impact of risk outcomes is technically...

Various concepts appeared in the existing literature to evaluate the risk exposure of a financial or insurance firm/subsidiary/line of business due to the occurrence of some extreme scenarios. Many of those concepts, such as Marginal Expected Shortfall or Tail Conditional Expectation, are simply...

Recently, a lot of attention has been focused on developing portfolio allocation models that take into account the asymmetric nature of asset return distributions. In this paper, we extend Krokhmal, Palmquist, and Uryasev's approach by using CVaR-like constraints in the traditional portfolio...

A critical problem in risk analysis involving financial variables is the calculation of risk margins. When there are a number of risks, the total risk margin is often reduced to reflect "diversification benefits." How large should the diversification benefit be? And how should the benefit be...

The 2015 Paris Agreement is a landmark in limiting emissions and targeting global warming well below 2, preferably 1.5, degrees Celsius compared to pre-industrial levels. In this light, we investigate how to efficiently construct equity portfolios that help mitigating climate change risk but at...