Actuarial Graduate Students Presentations

Actuarial Graduate Students Presentations
Chair: Étienne Marceau (Université Laval)
Organizer: Hélène Cossette (Université Laval)

SABRINA ZHANG, Simon Fraser University
The Optimal Payment Reduction Ratios For a Catastrophe Bond.  [PDF]

Catastrophe bonds are insurance-linked securities that transfer catastrophe risks from insurance industry to bond holders. If there is a catastrophe, the catastrophe bond is triggered and the future bond payments are reduced. This paper first presents a general pricing formula for a catastrophe bond with coupon payments, adaptable to various assumptions for a catastrophe loss process. Next, it gives formulas for the optimal payment reduction ratios which maximize two measurements of risk reduction, hedge effectiveness rate (HER) and hedge effectiveness (HE), respectively, and examines how the optimal payment reduction ratios help reinsurers or insurers to mitigate extreme losses. Last, it shows how the parameters of the models affect the optimal payment reduction ratios with numerical examples for illustrations.

JI RUAN-CANCELLED, University of Calgary
Cluster Analysis of Gene Expression Profiles via Flexible Count Models for RNA-seq Data  [PDF]

Clustering RNA-seq data is used to characterize environment-induced (e.g., treatment) differences in gene expression profiles by separating genes into clusters based on their expression patterns. Wang et al. (2014) recently adopted the bivariate Poisson (BVP) distribution, obtained via the trivariate reduction method, as a model for clustering bivariate RNA-seq data. We discuss the inadequacy of BVP in modelling the correlation between bivariate counts, and its impact on clustering such data. We introduce an alternative Gaussian copula model (GCM) that incorporates a flexible dependence structure for the counts, and report simulation results to compare the performance of GCM and BVP and investigate the impact on clustering of Poisson counts of misspecified dependence structures. We illustrate our methodology on real RNA-seq data.

Credit Risk in Corporate Spreads during the Financial Crisis of 2008  [PDF]

Credit spreads and CDS premiums are investigated before, during and after the financial crisis with a flexible credit risk model. The latter is designed to capture empirical facts: a regime-switching framework adjusts its behaviour to the financial cycles and the negative relationship between recovery rates and default probabilities appears endogenously.

Using a firm-by-firm estimation of 225 companies, notorious empirical questions are revisited, including the famous credit spread puzzle. The proportion of the spread explained by credit risk decreases during the crisis. Liquidity plays a significant role in explaining this gap throughout the financial turmoil and persists thereafter.

ITRE MTALAI, Université Laval
Aggregation Methods for Portfolios of Dependent Risks with Archimedean Copulas  [PDF]

In this paper, we consider a portfolio of dependent risks represented by a vector of dependent random variables (rvs) whose joint cumulative distribution function (cdf) is defined with an Archimedean copula. Archimedean copulas are very popular and their extensions, nested Archimedean copulas, are well suited for vector of rvs of high dimension. We examine the computation of the cdf of the sum or a variety of functions of those rvs. In particular, we derive the cdf and the TVaR of the sum of those risks using the Frank copula and the Ali-Mikhail-Haq (AMH) copula. The computation of the contribution of each risk under the TVaR-based allocation rule, the covariance allocation rule and the Esscher-based allocation rule is also treated.

MIRABELLE HUYNH, University of Waterloo
On a Risk Model with Claim Investigation  [PDF]

A queue-based claims investigation mechanism is assumed for the insurer's claims payment process to model its claim adjustment practices. The resulting model may be viewed as a first step in developing models with more realistic claim investigation mechanisms. Claim settlement delays and time dependent payments have been studied by, e.g., Taylor [1979], Cai and Dickson [2002], and Trufin et al. [2011]. However, little has been done on queue-based investigation mechanisms. We demonstrate the impact of a simple claim investigation mechanism on some common ruin-related quantities of interest when claims are assumed to occur according to a Poisson process. An exponentially distributed investigation time is considered. We conclude with numerical examples where we explore questions arising from a risk management standpoint.

YISUB KYE, York University
On the probability of ruin for non-identically distributed and dependent claims  [PDF]

In this talk I will consider a continuous risk model with positively dependent and non-identically distributed claim amounts. More specifically, I'll discuss the derivation of the expressions for the ruin probability at or before a certain claim arrival instant in the situations when claim numbers follow a renewal process with either Erlang or a mixture of exponentials inter-arrival times. I will elucidate the finding with the help of numerical examples.

This is a joint work with Ed Furman of York U,Toronto, Canada and Raluca Vernic of the Institute for Mathematical Statistics and Applied Mathematics, Bucharest, Romania.