The optimal reinsurance contract is investigated from the perspective of an insurer who would like to minimise its risk exposure under Solvency II. Under this regulatory framework, the insurer is exposed to the retained risk, reinsurance premium and change in the risk margin requirement as a...

Asymptotic results are obtained for several conditional measures of association. The chosen random variables are the first two order statistics and the total sum within a random sum. Many of the results have confirmed the “one-jump” property of the risk model. Non-trivial limits are obtained...

Asymptotic tail probabilities for linear combinations of randomly weighted order statistics are approximated under various assumptions. One key assumption is the asymptotic independence for all risks. Therefore, it is not surprising that the maxima represents the most influential factor when one...

This paper studies the set of Pareto optimal insurance contracts and the core of an insurance game. Our setting allows multiple insurers with translation invariant preferences. We characterise the Pareto optimal contracts, which determines the shape of the indemnities. Closed-form and numerical...

Systemic risk (SR) has been shown to play an important role in explaining the financial turmoils in the last several decades and understanding this source of risk has been a particular interest amongst academics, practitioners, and regulators. The precise mathematical formulation of SR is still...

In various fields of applications such as capital allocation, sensitivity analysis and systemic risk evaluation, one often needs to compute or estimate the expectation of a random variable given that another random variable is equal to its quantile at some pre-specified probability level. A...

The risk exposure of a business line could be perceived in many ways and is sensitive to the exercise that is performed. One way is to understand the effect of some common/reference risk over the performance of the business line in question, but irrespective of the modelling exercise, the...

Decision-makers who usually face model/parameter risk may prefer to act prudently by identifying optimal contracts that are robust to such sources of uncertainty. In this paper, we tackle this issue under a finite uncertainty set that contains a number of probability models that are candidates...

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...

Capital efficiency and asset/liability management are part of the Enterprise Risk Management Process of any insurance/reinsurance conglomerate and serve as quantitative methods to fulfill the strategic planning within an insurance organisation. There has been a considerable amount of work in...