Recent Advances in Predictive Methods in Actuarial Science

Recent Advances in Predictive Methods in Actuarial Science
Organizer and Chair: Manuel Morales (Université de Montréal)

CARY TSAI, Simon Fraser University
A Linear Relational Approach to Modelling Mortality Rates  [PDF]

In this talk, we first briefly introduce two well-known mortality models, the Lee-Carter model and the CBD model. Then a linear relational approach based on simple linear regression to modelling mortality rates is proposed, which linearly relates one mortality sequence to the other of equal length with the evidence of observations from empirical mortality data. Some variations and applications are given, and forecasting performances among models are also compared with numerical illustrations.

MACIEJ AUGUSTYNIAK, Université de Montréal
Estimating the Markov-Switching GARCH Model with a Deterministic Particle Filter  [PDF]

The Markov-switching GARCH model allows for a GARCH structure with time-varying parameters. This flexibility is unfortunately undermined by a path dependence problem which complicates the parameter estimation process. This problem led to the development of computationally intensive estimation methods and to simpler techniques based on an approximation of the model, known as collapsing procedures. This article develops an original algorithm to conduct maximum likelihood inference in the Markov-switching GARCH model, generalizing and improving previously proposed collapsing approaches. A new relationship between particle filtering and collapsing procedures is established which reveals that this algorithm corresponds to a deterministic particle filter. Simulation and empirical studies show that the proposed method allows for a fast and accurate estimation of the model.

Predicting Best-Estimate Yield Curves in Incomplete Bond Markets  [PDF]

The concept of best-estimate, prescribed by regulators to value insurance liabilities for accounting and solvency purposes, has recently been discussed extensively in the insurance industry and related academic literature. Happ, Merz and Wüthrich (2014) define best-estimates using orthogonal projections of a claim on the space of replicable payoffs. In this paper, we apply the concept of best-estimates to long-maturity claims in a market with reinvestment risk. We assume that a limited number of short-maturity bonds are traded, and derive the best-estimate price of bonds with longer maturity, thus obtaining a best-estimate yield curve. We derive expressions for the price of the long-term bond under the multifactor Vasicek model.