Actuarial Models The Mathematics Of Insurance Second Edition Pdf


	February 3, 2012 Second Québec-Ontario Workshop on Insurance Mathematics Fields Institute, 222 College St. Toronto Organizing Committee Andrei Badescu (University of Toronto) David Landriault (University of Waterloo) Sheldon Lin (University of Toronto) Manuel Morales (Université de Montréal) Jean-François Renaud (UQAM), Gordon Willmot (University of Waterloo)	Department of Statistics, University of Toronto

Objectives

The 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 non-life 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 up-and-coming 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 high-profile 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 Québec-Ontario area (as well as outside of these two provinces).

Speakers

Keynote speaker:
Jose Garrido (Concordia University)

Invited speakers:
Maciej Augustyniak (Université de Montréal)
Mathieu Boudreault (UQAM)
Hélène Cossette (Université Laval)
Sebastian Jaimungal (University of Toronto)
Bruce Jones (University of Western Ontario)
Hyejin Ku (York University)
Khouzeima Moutanabbir (Université Laval)
David Saunders (University of Waterloo)
Wei Wei (University of Waterloo)

Scientific Program
audio and slides available here

Friday February 3, 2012
8:30-8:50	Registration
8:50-9:00	Opening remarks
SESSION 1
9:00-10:00	José Garrido (Concordia University)
10:00-10:30	David Saunders (University of Waterloo)
10:30-11:00	Coffee break
SESSION 2
11:00-11:30	Bruce L. Jones (University of Western Ontario)
11:30-12:00	Khouzeima Moutanabbir (University Laval)
12:00-12:30	Mathieu Boudreault (UQAM)
12:30-2:00	Lunch at Fields
SESSION 3
2:00-2:30	Hélène Cossette (University Laval)
2:30-3:00	Wei Wei (University of Waterloo)
3:00-3:30	Hyejin Ku (York University)
3:30-4:00	Coffee Break
SESSION 4
4:00-4:30	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)

Speaker Abstracts

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 risk-free profit at zero cost. The existence of such classical arbitrage opportunities can arise from over- or under-estimation 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.

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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 lead-up 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.
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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).
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Khouzeima Moutanabbir (Université Laval)

Asset-liability 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 multi-stage 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.
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Mathieu Boudreault (UQAM)

Multivariate integer-valued 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 integer-valued 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 short-term. 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.
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Hélène Cossette (Université Laval)

Analysis of the discounted sum of ascending ladder heights
Within the Sparre-Andersen 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 infinite-time intervals. In particular, the moments of the discounted sum of ascending ladder heights over finite- and infinite-time intervals are derived in both the classical compound Poisson risk model and the Sparre-Andersen risk model with exponential claims. The application of a particular Gerber-Shiu 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 moment-matching method to approximate the distribution of the discounted sum of ascending ladder heights allowing the computation of the VaR and TVaR risk measures.
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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.
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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 Cetin-Jarrow-Protter, 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.
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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 path-dependent products through re-writing 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).
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Maciej Augustyniak (Université de Montréal)

Estimation of a path dependent RS-GARCH model by a Monte Carlo EM algorithm

Regime-switching generalized autoregressive conditional heteroskedasticity (RS-GARCH) 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 RS-GARCH 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 RS-GARCH model without resorting to some sort of modification of the model. In this presentation, I propose a novel approach based on the Monte Carlo expectation-maximization algorithm to estimate the MLE. Practical implementation of this method and its effectiveness in recovering the MLE are studied.
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Confirmed Participants as of January 31, 2012

Full Name	University/Affiliation
Abdallah, Anas	Universit� Laval
Al Jarousha, Ayat	University of Western Ontario
Augustyniak, Maciej	Universit� de Montr�al
Badescu, Andrei	University of Toronto
Bernard, Carole	University of Waterloo
Bosch Frigola, Irene	Concordia University
Boucher, Jean-Philippe	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, H�l�ne	Laval University
Cousineau, Alexandre	Universit� de Montr�al
Donnelly, Ryan	University of Toronto
Elmahdaoui, Raymond	University of Montreal
Gao, Huan	University of Western Ontario
Garrido, Jos�	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, M�lina	Universit� Laval
Marceau, Etienne	Universit� Laval
Morales, Manuel	Universit� de Montr�al
Moutanabbir, Khouzeima	Laval University
Qian, Cheng	University of Western Ontario
Ren, Jiandong	University of Western Ontario
Renaud, Jean-Fran�ois	Universit� du Qu�bec � Montr�al
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

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