2016-Actuarial Science and Finance 1

Actuarial Science and Finance 1 
Chair: Étienne Marceau (Laval University) 

NICHOLAS BECK, McGill University
A Consistent Estimator to the Orthant-Based Tail Value-at-Risk  [PDF]
In this paper we address the estimation of multivariate Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR). We recall definitions for the bivariate lower and upper orthant VaR and bivariate lower and upper orthant TVaR, presented in Cossette et al. (2013, 2014). Here, we present estimators for both these measure extended to arbitrary dimension d>2 and establish the consistency of our estimator for the lower and upper orthant TVaR in any dimension. We then demonstrate these results by providing numerical examples that compare our estimator to theoretical results, from both real and simulated data. 
Credit and Systemic Risks in the Financial Services Sector  [PDF]
The Great Recession has shaken the foundations of the financial industry and led to tighter solvency monitoring of both the banking and insurance industries. To this end, we develop a portfolio credit risk model that includes firm-specific Markov-switching regimes as well as individual stochastic and endogenous recovery rates. Using weekly credit default swap premiums for 35 financial firms, we analyze the credit risk of each of these companies and their statistical linkages, placing special emphasis on the 2005-2012 period. Moreover, we study the systemic risk affecting both the banking and insurance subsectors. 
LICHEN CHEN, University of Waterloo
Bayesian Estimation of GARCH Models with General Parameter Constraints  [PDF]
We discuss Bayesian estimation of GARCH models with general parameter constraints for non-negative conditional variance. The general parameter constraints are important for capturing long-memory type behaviour of financial asset return volatilities together with their short-term behaviour. However, the shapes of the parameter space and the likelihood surface under these constraints often pose computational problems to standard estimation algorithms. In our work we explain how Bayesian MCMC methods and model reparameterization can help us solve these difficulties. 
WENJUN JIANG, Western University
Optimal Reinsurance Minimizing the Risk of Joint Party  [PDF]
Optimal reinsurance problem has been studied for a long time. By imposing restrictions on ceded function, analytical solutions can be obtained under certain risk measures. However, most studies are from the viewpoint of insurer or reinsurer. In this paper, we consider the bivariate Value-at-Risk of joint party, insurer and reinsurer, and take full use of geometric approach to obtain the optimal form of reinsurance with ceded function in C1 and C2 [Chi and Tan~(2011)]. We further illustrate the solution is also Pareto-optimal and derive the optimal reinsurance parameters. 
LUYAO LIN, Simon Fraser University
Analysis of Survivorship Life Insurance Portfolio with Stochastic Interest Rates  [PDF]
A general portfolio of joint survivorship life insurance contracts is studied in a stochastic interest rate environment with dependent mortality model. Two methods are used to derive the first two moments of the projected prospective loss random variable. The distribution function of the present value of future losses at given valuation time is derived and approximated for a homogeneous portfolio. The effects of the mortality dependence, the portfolio size and the policy type, as well as the impact of investment strategies on the riskiness of portfolios of survivorship life insurance policies are analyzed by means of moments and probability distributions. 
YING WANG, University of Waterloo
Fair Premium for Reinsurance Contracts  [PDF]
Fair reinsurance premium principles considering risks of both insurer and reinsurer are introduced. Scholars usually investigate the optimal ceded function if the reinsurance premium is given. In this paper, quadratic and identity loss functions are applied to quantify the risks of both insurer and reinsurer. And two novel reinsurance premium principles are proposed. In addition, the properties for these two kinds of premium principles are studied.