April 18, 2014

Thematic Program on Quantitative Finance:
Foundations and Applications January - June, 2010

June 21, 2010
Industrial-Academic Forum on
Financial Engineering and Insurance Mathematics

Organizers: H. Huang, M. Milevsky,
T. Salisbury (York )

Supported by :

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The industrial Academic (IA) forum is intended to allow University researchers in the field of finance & insurance mathematics (FinSurance) to interact with practitioners in the field. The morning (9am to 12:30pm) will consist of a number of high-profile plenary talks of approximately 60 minutes each, with amply time allocated to questions and answers as well as dialogue with the audience. These presentations will be accessible and aimed at a wide audience, with particular emphasis on risk evaluation and management for insurance companies issuing long-dated guarantees.

The afternoon session will consist of 5-7 shorter technical presentation of approximately 25 minutes each, primarily from junior researchers (post docs, PhD. students), also in the field of FinSurance. The organizers are currently soliciting speakers for the afternoon session and anyone interested in presenting is welcome to contact any one of the members of the organizing committee.



Arthur Fliegelman
A. Fliegelman & Associates, LLC

What Have We Learned in the Last Two Years: We Have Learned Haven't We?
Two years into the most severe financial crisis since the Great Depression, what have we learned, and for how long have we learned it? The “Great Moderation” led society into believing that economic cycles had been tamed or possibly even eliminated, and that associated risk levels had consequently declined to unprecedentedly low levels. We now know that economic cycles had not been tamed and that risk levels were actually much higher than were then believed with the resulting economic storm requiring virtually unprecedented levels of government intervention in worldwide financial systems. American life insurers as a whole, while very much impacted by the resulting economic tsunami, nonetheless performed better than many other types of financial institutions during this very difficult period. Insurers that were most adversely affected by the crisis typically exhibited the following behaviors:
(1) insufficient available liquidity especially at the holding company level;
(2) an expectation that high levels of equity risk could be managed through hedging or other similar programs; (3) a belief that increased levels of return on equity could be earned without incurring associated higher levels of risk; and (4) that excess capital could safely be used to fund stock repurchases or business acquisitions. Conversely, the most successful companies during this period were those that remained conservatively managed with sufficient internal flexibility to manage through extreme events without inflicting excessive harm on the organization.

Stanley R. Pliska
co-authors: I. Duarte, D. Pinheiro, and A. A. Pinto

Optimal Life Insurance, Consumption and Investment
We consider the problem of a wage earner who wants to make optimal, lifetime financial planning decisions for his family. With a random lifetime and given a specified income stream, he wants to purchase life insurance to protect his family against his death before retirement. He also invests a portion of his salary in a riskless asset as well as in a number of risky assets, and the balance of his income is consumed. The wage earner's problem is to find the optimal consumption, investment, and insurance purchase decisions in order to maximize the expected utility of (1) consumption, (2) the size of his estate in the event of premature death, and (3) the size of the estate at the time of retirement if he lives that long. With the risky securities modeled as multidimensional geometric Brownian motion, dynamic programming methods are used to obtain explicit solutions in the case of constant relative risk aversion utility functions, and some new results are presented together with the corresponding economic interpretations.

Robert R. Reitano
Professor of the Practice in Finance, Brandeis University

Risk Management of Long Liabilities in Insurance and Pensions
We begin with a brief introduction to the most common types of long financial liabilities and their risk attributes, as well as to the risk attributes of potential funding assets, and quantify how these risk attributes can compound or counteract in terms of the associated effects on risk to economic capital. These general ideas will then be illustrated in detail with two examples. The first example will focus on risk assessment and management for a Long Term Care (LTC) insurance block, focusing on an interest rate "hedging" model. Specifically, we illustrate an attempted interest rate hedge of a closed LTC block acquisition, evaluating the strengths and shortcomings of potential hedging approaches, and discuss the additional challenges associated with the issuance and hedging of incremental new business. The second example will address risk assessment and management for a Pension Plan, focusing on a "non-hedging funding" model. We begin with a hedge model assessment of risks, but focus on risk assessment within various typical “non-hedging” funding models. Within this framework, the focus is not on hedging the risks associated with guarantees, but on estimating the risk of plan failure.

Student Abstracts

Yuxiang Chong (University of Toronto)
Pricing catastrophe options under a regime-switching model
The catastrophe options distinguish between a loss period [0,T1],during which the catastrophes may happen, and a development period [T1,T2], during which losses entered before T1 are reestimated. In this paper, we will model cumulative catastrophe loss before T1 as a doubly stochastic Poisson process. In order to incorporate the seasonal effect on the occurrence of catastrophe events, we will let both the intensity of Poisson process and the distribution of jump size depend on the state of a continuous time Markov chain. During the development period, losses are reestimated by a geometric Brownian motion. In this setting we derive partial integro-differential equations for the prices of catastrophe options. Using Fourier transform techniques, we are able to provide analytical pricing formulas for catastrophe options.

Jessica Tsang Kwai Kew (York University)
Asset Allocation and Efficient Frontiers for Mortality Linked Securities
Investment in mortality-linked securities such as baskets of life settlements offer investors returns that are largely uncorrelated with other asset classes. The absence of academic work on the investment characteristics of such baskets is an obstacle to institutional investors entering this market. A Monte Carlo approach is used to quantify the diversification benefits in incorporating life settlement policies in a portfolio. The efficient frontier as well as questions concerning an optimum asset allocation when we combine these securities with equities and bonds in a portfolio is examined. In this presentation, I will introduce life settlement which is a financial arrangement when a third party buys the rights to the benefits of a life insurance policy from an insured individual or policyholder. I will also present some preliminary simulation results on how I model the behavior of a portfolio over a period of 10 years when we vary the initial allocation of equities/bonds and life settlements in the portfolio. Finally, I discuss what I plan to do next to extend this basic model into a more realistic model.

Zhongxian Men (University of Waterloo)
Multivariate stochastic volatility models: A Gibbs approach under the inverse Wishart distribution
Multivariate stochastic volatility (MSV) models have been intensively studied in the past several years. For the general case of the MSV models, there are not many methods having been proposed. In this talk, correlations are permitted between the innovations of the asset returns and those of the volatility dynamics. We look at the MSV model in a Bayesian framework by applying an inverse Wishart distribution. The multistage slice sampler within the Gibbs algorithm is proposed to sample the persistent parameters and latent variables. Since the Metropolis-Hastings (M-H) method is avoided, our algorithm is more efficient and easier to operate.

Eddie Ng (University of Toronto)
Kernel-based Copula Processes
The field of time-series analysis has made important contributions to a wide spectrum of applications such as tide-level studies in hydrology, natural resource prospecting in geo-statistics, speech recognition, weather forecasting, financial trading, and economic forecasts and analysis. Nevertheless, the analysis of the non-Gaussian and non-stationary features of time-series remains challenging for the current state-of-art models.
This work proposes an innovative framework which leverages the theory of copula, combined with a probabilistic framework from the machine learning community, to produce a versatile tool for multiple time-series analysis. I coined this new model Kernel-based Copula Processes (KCPs). Under the new proposed framework, various idiosyncracies can be modeled parsimoniously via a kernel function for individual time-series, and long-range dependency can be captured by a copula function. The copula function separates the marginal behavior and serial dependency structures, thus allowing them to be modeled separately and with much greater flexibility. Moreover, the codependent structure of a large number of time-series with potentially vastly different characteristics can be captured in a compact and elegant fashion through the notion of a binding copula. This feature allows a highly heterogeneous model to be built, breaking free from the homogeneous limitation of most conventional models. The KCPs have demonstrated superior predictive power when used to forecast a multitude of data sets from meteorological and financial areas. Finally, the versatility of the KCP model is exemplified when it was successfully applied to non-trivial classification problems unaltered.

Jinlian Wang (York University)
Ruin probability under stochastic mortality
Human beings are living longer than in the past. Their life expectancy has been improved significantly since last century. The demise of Defined Benefit Pensions forces more retirees to use defined contribution pension plan to hedge the longevity risk. So it's possible for the retirees to run out of wealth before run out of life while their current standard of living is maintained. Hence to provide retirement advice, life ruin probability becomes very important.
The stochastic hazard rate is studied when we compute life time ruin probability. This is reasonable since the hazard rate is not a constant, it has ups and downs. The problem is modeled using stochastic differential equations, which is solved by converting the probability into Partial Differential Equations (PDEs). Analytical solutions can not be found to these highly nonlinear equations and numerical methods are the only way to get the approximate ones. Alternative Direction Implicit (ADI) method and Upwind Scheme are chosen to solve the 2D ruin problem. These have significantly reduced the computing time and saved lots of space.
The ruin probability under stochastic hazard rate and deterministic hazard rate is compared. When the stochastic hazard rate collapses to Gompertz Distribution, these two probabilities match very well. The effect of the correlation between wealth and hazard rate is studied. Our results show that when the correlation is positive, the ruin probability is higher, which is consistent to the commonsense.



9:15 Opening remarks (Grasselli, Milevsky)
9:20-10:10 Robert R. Reitano
Risk Management of Long Liabilities in Insurance and Pensions
10:15-11:05 Arthur Fliegelman
What Have We Learned in the Last Two Years: We Have Learned Haven't We?
11:10-12:00 Stanley R. Pliska
Optimal Life Insurance, Consumption and Investment
12-1 Lunch
1:00 - 1:20 Eddie Ng (University of Toronto)
Kernel-based Copula Processes
1:20 - 1:40 Jessica Tsang Kwai Kew (York University)
Asset Allocation and Efficient Frontiers for Mortality Linked Securities
1:40 - 2:00 Zhongxian Men (University of Waterloo)
Multivariate stochastic volatility models: A Gibbs approach under the inverse Wishart distribution
2:00 - 2:10 Break
2:10 - 2:30 Jinlian Wang (York University)
Ruin probability under stochastic mortality
2:30 - 2:50 Yuxiang Chong (University of Toronto)
Pricing catastrophe options under a regime-switching model
2:50 - 3:00 Discussion


Confirmed Participants

Full Name University/Affiliation
Bae, Tae Han Algorithmics Inc.
Chan, Paul TD Securities
Cheng, Wayne S. TD Bank Financial Group
Chong, Yuxiang University of Toronto
Dabrowski, Simon York University
Depoe, Kiel York University
Fahim, Arash Ecole Polytechnique
Fliegelman, Arthur A. Fliegelman & Associates, LLC
Fu, Stephen TD Bank Financial Group
Gapeev, Pavel London School of Economics
Grasselli, Matheus McMaster University
Grzesik, Robert York University
Guo, Weiwei University of Toronto
Habib, Faisal QWeMA Group, Inc.
Halaj, Grzegorz ALM in Bank Pekao (UniCredit Group)
Halaj, Grzegorz ALM in Bank Pekao (UniCredit Group)
Holm, Philip TD Bank Financial Group
Huang, Haohan York University
Huang, Huaxiong York University
Hughston, Lane Imperial College
Hurd, Tom McMaster University
Kang, John York University
Lin, X. Sheldon University of Toronto
Macqueen, Alexandra QWeMA Group, Inc.
Mausser, Helmut Algorithmics Incorporated
Milevsky, Moshe York University, Schulich School of Business
Mohandas, Deepesh York University
Ng, Eddie K.H. University of Toronto
O'Brien, Jonathan University of Toronto
Odette, Lou Massachusetts Institute of Technology
Peng, Xianhua Fields Institute and York University
Platen, Eckhard University of Technology Sydney
Pliska, Stanley R. University of Illinois at Chicago
Poon, Kingswood TD Bank Financial Group
Qiu, Daria York University
Reitano, Robert R. Brandeis University
Salisbury, Thomas York University
Shan, Yan York University
Sharma, Rita York University
Silla, Sebastiano Polytechnic University of Marche
Singh, Arjun York University
Straus, Daniel York University
Touzi, Nizar Ecole Polytechnique
Wang, Bei York University
Wang, Hao York University
Wang, Jinlian York University
Wiese, Anke Heriot-Watt University
Wu, Panpan University of Toronto
Xue, Feifei York University
Yu, Ying Boston University
Zubelli, Jorge IMPA


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