On modeling quantities for insurer solvency against catastrophe under some Markovian assumptions

Insurance companies sometimes face catastrophic losses, yet they must remain solvent enough to meet the legal obligation of covering all claims. Catastrophes can result in large damages to the policyholders, causing the arrival of numerous claims to insurance companies at once. Furthermore, the severity of an event could impact the time until the next occurrence. An insurer needs certain levels of startup capital to meet all claims, and then must have adequate reserves on a continual basis, even more so when catastrophes occur. This work examines two facets of these matters: for an infinite time horizon, we extend and develop models for insurer bankruptcy-related quantities accounting for the reality of large claims occurring. Meanwhile, for finite time horizons, we model the present value of claims that have been incurred but not yet reported, so-called \u27IBNR\u27 claims. In the former, we show how our method for \u27Gerber-Shiu\u27 functions works in a recently proposed dependency structure allowing insurers to charge clients different premiums depending on their riskiness. In the latter, we build upon a recent method which allowed claims to arrive in batches; besides permitting discounting to be time-dependent, we allow the insurer to adjust the assumed distribution of the time until the next event by comparing the number of claims from the current event to any number of random intervals. We provide numerical studies for both scenarios --Abstract, page iii

Plasticity of Amino Acid Residue 145 Near the Receptor Binding Site of H3 Swine Influenza A Viruses and Its Impact on Receptor Binding and Antibody Recognition.

The hemagglutinin (HA), a glycoprotein on the surface of influenza A virus (IAV), initiates the virus life cycle by binding to terminal sialic acid (SA) residues on host cells. The HA gradually accumulates amino acid substitutions that allow IAV to escape immunity through a mechanism known as antigenic drift. We recently confirmed that a small set of amino acid residues are largely responsible for driving antigenic drift in swine-origin H3 IAV. All identified residues are located adjacent to the HA receptor binding site (RBS), suggesting that substitutions associated with antigenic drift may also influence receptor binding. Among those substitutions, residue 145 was shown to be a major determinant of antigenic evolution. To determine whether there are functional constraints to substitutions near the RBS and their impact on receptor binding and antigenic properties, we carried out site-directed mutagenesis experiments at the single-amino-acid level. We generated a panel of viruses carrying substitutions at residue 145 representing all 20 amino acids. Despite limited amino acid usage in nature, most substitutions at residue 145 were well tolerated without having a major impact on virus replication in vitro All substitution mutants retained receptor binding specificity, but the substitutions frequently led to decreased receptor binding. Glycan microarray analysis showed that substitutions at residue 145 modulate binding to a broad range of glycans. Furthermore, antigenic characterization identified specific substitutions at residue 145 that altered antibody recognition. This work provides a better understanding of the functional effects of amino acid substitutions near the RBS and the interplay between receptor binding and antigenic drift.IMPORTANCE The complex and continuous antigenic evolution of IAVs remains a major hurdle for vaccine selection and effective vaccination. On the hemagglutinin (HA) of the H3N2 IAVs, the amino acid substitution N 145 K causes significant antigenic changes. We show that amino acid 145 displays remarkable amino acid plasticity in vitro, tolerating multiple amino acid substitutions, many of which have not yet been observed in nature. Mutant viruses carrying substitutions at residue 145 showed no major impairment in virus replication in the presence of lower receptor binding avidity. However, their antigenic characterization confirmed the impact of the 145 K substitution in antibody immunodominance. We provide a better understanding of the functional effects of amino acid substitutions implicated in antigenic drift and its consequences for receptor binding and antigenicity. The mutation analyses presented in this report represent a significant data set to aid and test the ability of computational approaches to predict binding of glycans and in antigenic cartography analyses