
COMMERCIAL AND INDUSTRIAL MATHEMATICS 

February 5, 2023  
ObjectivesThe primary aim of this workshop is to provide a venue for academics, including graduate students and postdoctoral fellows, to meet and discuss their latest research topics in the broad area of insurance mathematics and its related disciplines (e.g. mathematical finance, applied probability and statistics). The workshop does not have a unique theme and/or topic in mind, but is intended to cover a rather broad scope of research interests in the general area of actuarial science. Among others, this includes life and nonlife insurance, risk management in insurance and finance, risk and ruin theory, financial modelling and applications of statistical methods in insurance. As for the first edition of this workshop, one of the main objectives of the second edition is to give the opportunity to the upandcoming researchers in the provinces of Québec and Ontario to promote their research program and facilitate their integration into the actuarial academic community in Canada and abroad. As such, the workshop plans to actively involve graduate students and postdoctoral fellows in its scientific program. This will provide a natural platform for these individuals to present their most recent research contributions to an audience of experts in the field of insurance mathematics. Also, young faculty will be invited to play a preponderant role in the scientific program. Canada has been known for years to be a stronghold of the actuarial science profession with many highprofile academics among its ranks. As such, our goal is to take advantage of Canada's unique feature in this regard and ensure continuity through the development of a strong cohort of young actuarial science academics.The workshop also intends to stimulate interaction and scientific collaboration, and foster relations of an academic and professional nature among the actuarial science groups in the QuébecOntario area (as well as outside of these two provinces). Speakers
Scientific Program

Friday February 3, 2012  
8:308:50  Registration 
8:509:00  Opening remarks 
SESSION 1  
9:0010:00  José Garrido (Concordia University) 
10:0010:30  David Saunders (University of Waterloo) 
10:3011:00  Coffee break 
SESSION 2  
11:0011:30  Bruce L. Jones (University of Western Ontario) 
11:3012:00  Khouzeima Moutanabbir (University Laval) 
12:0012:30  Mathieu Boudreault (UQAM) 
12:302:00  Lunch at Fields 
SESSION 3  
2:002:30  Hélène Cossette (University Laval) 
2:303:00  Wei Wei (University of Waterloo) 
3:003:30  Hyejin Ku (York University) 
3:304:00  Coffee Break 
SESSION 4  
4:004:30  Sebastian Jaimungal (University of Toronto) 
4:30 5:00  Maciej Augustyniak (University de Montréal) 
RECEPTION  
6:00  10:00  Cocktail Hour followed by Buffet Dinner at 7:00 (The Faculty Club, University of Toronto, 41 Willcocks Street) 
Keynote Speaker: José Garrido (Concordia
University)
Credit risk; a complex system seen from an actuarial perspective
Credit risk models share several common characteristics with actuarial risk
theory models. Even if the problems studied with these models are different,
their solutions are similar in some respects. In modern science, risk credit
could be considered a complex system, where it is not sufficient to isolate
the effect of a single factor on the risk credit quantity of interest (like
the probability of default on a corporate bond). Rating agencies, like Moody`s
or Standard and Poor`s use complex econometrical models with several variables,
some quite subjective, to come up with their credit ratings. We propose to
revisit the problem with a more classical actuarial approach.
In classical finance, a consistent market is in balance if it does not let agents take advantage of price differences to make a riskfree profit at zero cost. The existence of such classical arbitrage opportunities can arise from over or underestimation of the underlying risk, like with current credit ratings on European governments bonds, indicating inefficiencies in the market. As an alternative to the classical arbitrage methods to deal with this problem, we introduce a new ranking based on risk measures.
We first introduce a new type of arbitrage defined from the properties of
risk measures. That is, if under a specific risk measure, the risk of a portfolio
is less than or equal to zero, then a possible positive portfolio income is
considered as an arbitrage income. Inconsistencies in bond markets refer to
the existence of these arbitrage opportunities. A new tool to detect and measure
these is established. Numerical examples with corporate bonds will serve to
illustrate the ideas.

David Saunders (University of Waterloo)
Mathematical and Computational Issues in Calculating Capital for Credit
Risk
The inadequacies of methods for calculating credit risk capital, particularly
in the trading book, in the leadup to the global financial crisis have led
to a reevaluation of regulatory capital, resulting in the new Basel III requirements.
I will discuss mathematical and computational problems that arise when computing
the new capital requirements for credit risk in the trading book.

Bruce L. Jones (University of Western Ontario)
Credibility for Pension Plan Terminations
In establishing demographic assumptions for pension plan calculations,
pension actuaries must decide on suitable termination rates. These rates typically
depend on age and years of service, but may also depend on other factors such
as economic conditions.
Restricting our attention to terminations other than mortality, disability
or retirement (i.e. resignations and firings), we investigate an approach
to adjusting a standard termination table to reflect the experience of the
plan and other variables. Actual to expected ratios are modeled using a generalized
linear model, and a limited fluctuation approach is used to reflect the credibility
of the plan experience.
This is joint work with Chou Chio Leong (University of Western Ontario).

Khouzeima Moutanabbir (Université
Laval)
Assetliability management for pension fund using an international investment
model
We introduce an asset liability model using stochastic programming. We
use an international investment model where investors are allowed to hold
assets in both domestic and foreign economies. We formulate a multistage
optimization problem for pension fund asset liability management and we provide
a solution based on scenario generation and stochastic programming. The model
is calibrated to Canadian and American data.

Mathieu Boudreault (UQAM)
Multivariate integervalued autoregressive models applied to earthquake
occurrences
In various situations in the insurance industry, in finance, in epidemiology,
etc., one needs to represent the joint evolution of the number of occurrences
of an event. In this paper, we present a multivariate integervalued autoregressive
(MINAR) model, derive its properties and apply the model to earthquake occurrences
across various pairs of tectonic plates. The model is an extension of Pedeli
& Karlis (2011) where cross autocorrelation (spatial contagion in a seismic
context) is considered. We fit various bivariate count models and find that
for many contiguous tectonic plates, spatial contagion is significant in both
directions. Furthermore, ignoring cross autocorrelation can underestimate
the potential for high numbers of occurrences over the shortterm. Our overall
findings seem to further confirm Parsons & Velasco (2011), meaning that
reinsurance companies can still diversify earthquake risk across different
regions of the planet.

Hélène Cossette (Université
Laval)
Analysis of the discounted sum of ascending ladder heights
Within the SparreAndersen risk model, the ruin probability corresponds to
the survival function of the maximal aggregate loss. It is well known that
the maximum aggregate loss follows a compound geometric distribution, in which
the summands consists of the ascending ladder heights. We propose to investigate
the distribution of the discounted sum of ascending ladder heights over finite
or infinitetime intervals. In particular, the moments of the discounted sum
of ascending ladder heights over finite and infinitetime intervals are derived
in both the classical compound Poisson risk model and the SparreAndersen
risk model with exponential claims. The application of a particular GerberShiu
functional is central to the derivation of these results, as is the mixed
Erlang distributional assumption. Finally, we define VaR and TVaR risk measures
in terms of the discounted sum of ascending ladder heights. We use a momentmatching
method to approximate the distribution of the discounted sum of ascending
ladder heights allowing the computation of the VaR and TVaR risk measures.

Wei Wei (University of Waterloo)
Optimal Allocations of deductibles and policy limits with generalized dependence structures
Optimal allocations of deductibles and policy limits have been studied by Cheung (2007), Hua and Cheung (2008 a, b), and Zhuang et al. (2008) among many others. In those literatures, only independent and comonotonic structures have been taken into considerations. This paper aims to develop a generalized dependence structure so as to unify and generalize the studies in the previous models.
Motivated by the bivariate characterizations of likelihood ratio order and
joint likelihood ratio order (Shanthikumar and Yao (1991)), we employ the
concept of arrangement increasing to define dependence between multivariate
random variables. Specifically, we associate arrangement increasing survival
functions and arrangement increasing joint density function with two different
dependence structures (SAI and UOAI) respectively, both of which include independence
and comonotonicity as special cases. It turns out that most results derived
in Cheung (2007), Hua and Cheung (2008 a, b), and Zhuang et al. (2008) are
preserved under these dependence structures. Namely, the deductibles or policy
limits could be ordered accordingly. We also solve a more general optimal
allocation problem under the dependence of SAI.

Hyejin Ku (York University)
Discrete Time Pricing and Hedging of Options under Liquidity Risk
Liquidity risk is the additional risk in a financial market due to the timing
and size of a trade. In the past decade, the literature on the liquidity risk
has been growing rapidly. Built on the asset pricing theory developed by CetinJarrowProtter,
we study how the classical hedging strategies should be modified and how the
prices of derivatives should be changed in the presence of liquidity costs,
especially when we hedge only at discrete time points.

Sebastian Jaimungal (University of Toronto)
Valuing GWBs with Stochastic Interest Rates and Volatility
Abstract: Guaranteed withdrawal benefits (GWBs) are long term contracts which provide investors with equity participation while providing them a secured income stream. Due to the long investment horizons involved, stochastic volatility and stochastic interest rates are important factors to include in their valuation. Here, we provide an efficient method for valuing these pathdependent products through rewriting the problem in the form of an Asian styled claim and a dimensionally reduced PDE. The PDE is then solved using an Alternating Direction Implicit (ADI) method. Furthermore, we derive an analytical closed form approximation and compare the approximate, as well as the results from the ADI method, with Monte Carlo simulations. We illustrate the various effects of the parameters on the valuation through numerical experiments and discuss their financial implications.
This is joint work with Dmitri Rubisov (BMO Capital Markets) and Ryan Donnelly
(University of Toronto).

Maciej Augustyniak (Université de
Montréal)
Estimation of a path dependent RSGARCH model by a Monte Carlo EM algorithm
Regimeswitching generalized autoregressive conditional heteroskedasticity
(RSGARCH) models are becoming increasingly popular to model financial data
in the econometric literature. Estimating these models is a challenging task
because the path dependence element of these models renders the exact computation
of the likelihood infeasible in practice. This led some authors to propose
estimation methods that do not depend on the likelihood such as a generalized
method of moments procedure and a Bayesian algorithm. Other authors suggested
estimating by maximum likelihood modified versions of the RSGARCH model that
avoid the path dependence problem. However, there is not yet a method available
to obtain the maximum likelihood estimator (MLE) of the path dependent RSGARCH
model without resorting to some sort of modification of the model. In this
presentation, I propose a novel approach based on the Monte Carlo expectationmaximization
algorithm to estimate the MLE. Practical implementation of this method and
its effectiveness in recovering the MLE are studied.

Full Name  University/Affiliation 
Abdallah, Anas  Université Laval 
Al Jarousha, Ayat  University of Western Ontario 
Augustyniak, Maciej  Université de Montréal 
Badescu, Andrei  University of Toronto 
Bernard, Carole  University of Waterloo 
Bosch Frigola, Irene  Concordia University 
Boucher, JeanPhilippe  UQAM 
Boudreault, Mathieu  UQAM 
Chen, Bingzheng  Tsinghua University 
Chen, Yingying  University of Waterloo 
Cheng, Jianhua  Jilin University 
Cheng, Xiaohua  University of Western Ontario 
Chong, Yuxiang  University of Toronto 
Cossette, Hélène  Laval University 
Cousineau, Alexandre  Université de Montréal 
Donnelly, Ryan  University of Toronto 
Elmahdaoui, Raymond  University of Montreal 
Gao, Huan  University of Western Ontario 
Garrido, José  Concordia University 
Ge, Jing  University of Western Ontario 
Geng, Li  University of Western Ontario 
Gu, Zhimin  University of Western Ontario 
Guan, Jiali  University of Western Ontario 
Hackmann, Daniel  York University 
Han, Dezhao  Concordia University 
Hou, Xueting  University of Western Ontario 
Huang, Yue  Carleton University 
Hyun, Darae  University of Western Ontario 
Iftekhar, Aisha  
Jackson, Ken  University of Toronto 
Jaimungal, Sebastian  University of Toronto 
Jin, Shu  University of Western Ontario 
Jin, Tao  University of Western Ontario 
Jones, Bruce  University of Western Ontario 
Ke, Wanjun  University of Western Ontario 
Kim, Taehee Kyle  University of Western Ontario 
Kreinin, Alexander  Algorithmics Incorporated 
Ku, Hyejin  York University 
Kunka, Robert  University of Western Ontario 
Landriault, David  University of Waterloo 
Lee, Wing Yan  University of Waterloo 
Lemieux, Christiane  University of Waterloo 
Li, Dongchen  University of Waterloo 
Li, Shu  University of Waterloo 
Lin, X. Sheldon  University of Toronto 
Liu, Fangda  University of Waterloo 
Liu, Xiaoming  University of Western Ontario 
MacKay, Anne  University of Waterloo 
Mailhot, Mélina  Université Laval 
Marceau, Etienne  Université Laval 
Morales, Manuel  Université de Montréal 
Moutanabbir, Khouzeima  Laval University 
Qian, Cheng  University of Western Ontario 
Ren, Jiandong  University of Western Ontario 
Renaud, JeanFrançois  Université du Québec à Montréal 
Ricci, Jason  University of Toronto 
Rosu, Cristina  University of Waterloo 
Saunders, David  University of Waterloo 
Scott, Alexandre  University of Western Ontario 
Shi, Tianxiang  University of Waterloo 
Wei, Wei  University of Waterloo 
Willmot, Gordon  University of Waterloo 
Woo, Jae Kyung  Columbia University 
Wu, Panpan  University of Toronto 
Yang, Guang  University of Western Ontario 
Zang, Yanyan  University of Western Ontario 
Zhou, Xiaowen  Concordia University 