Asymptotic Tail Probability of the Discounted Aggregate Claims under Homogeneous, Non-Homogeneous and Mixed Poisson Risk Model

In this paper, we derive a closed-form expression of the tail probability of the aggregate discounted claims under homogeneous, non-homogeneous and mixed Poisson risk models with constant force of interest by using a general dependence structure between the inter-occurrence time and the claim sizes. This dependence structure is relevant since it is well known that under catastrophic or extreme events the inter-occurrence time and the claim severities are dependent.

The Opioid Crisis or Climate Change

Societal problems can occasionally have legal solutions, and several tools exist to implement change, including litigation and regulation. However, what elements make a societal problem more suitable for litigation or regulation? This Article examines four different societal issues (tobacco use, obesity, opioid addiction, and climate change) to determine whether litigation or regulation is the more appropriate route for success. The tobacco litigation serves as a successful example, while the fast food litigation serves as an unsuccessful example. Six signs of success are derived from the tobacco litigation: a large settlement agreement, evidence of corporate wrongdoing, change in public opinion, the litigation inspiring regulations, new courtroom avenues, and the ability to aggregate claims. The Article concludes that opioid litigation will be more successful under the tobacco litigation model than climate change litigation, because opioid litigation adapts the tobacco model to end the opioid epidemic. Novel solutions include utilizing Multi-District Litigation and the first-ever “negotiation class” that allows all 30,000 American cities to participate in a global settlement agreement with Big Pharma.

A Game Theoretic Analysis of the Relative Payouts to Operational Creditors and Financial Creditors from Bankruptcy Resolution in India

This paper analyses the outcomes of the cases resolved under Insolvency and Bankruptcy Code of India to examine the treatment of admitted claims for the two main classes of creditors i.e. operational and financial creditors. It shows that, at an aggregate level, operational creditors and financial creditors realize an equal percentage of their claims. However, at an individual level, there is wide heterogeneity in the treatment of the two classes of creditors. Three benchmark division rules – Proportional division, Constrained Equal Losses and Constrained Equal Awards, are used to characterize the actual divisions in each case. This analysis allows us to hypothesize that when aggregate claims of operational creditors are tiny, the Constrained Equal Awards (that is extremely generous to small creditors), does well. When aggregate claims of operational creditors are large, the Proportional rule does well. But when the claims of operational creditors fall in an intermediate range, the Constrained Equal Losses rule which is most unfavourable to the operational creditor comes to the fore. Hence, some broad guidelines that can be applied on a case by case basis appear to be desirable.

Precise large deviations for the aggregate claims in a dependent compound renewal risk model

We consider a dependent compound renewal risk model, where the interarrival times of accidents and the claim numbers follow a dependence structure characterized by a conditional tail probability and the claim sizes have a pairwise negatively quadrant dependence structure or a related dependence structure with the upper tail asymptotical dependence structure. When the distributions of the claim sizes belong to the dominated variation distribution class, we give the asymptotic lower and upper bounds for the precise large deviations of the aggregate claims.