Recent Advances in Actuarial Mathematics (15w5021)

Arriving in Oaxaca, Mexico Sunday, October 25 and departing Friday October 30, 2015


(Katholieke Universiteit)

(University of Toronto)

(University of Connecticut)


Actuarial science is principally concerned with risk and uncertainty; it is a unique discipline that applies mathematics, statistics, business and several other diverse disciplines in the measurement and understanding of risks. Apart from the usual construction of mathematical models, the science is equally concerned with the financial and economic outcome of risks. Although a discipline not widely popular to the layman, almost everybody on the planet is touched, affected and influenced by it. Everybody faces risks, or uncertain events, almost at every tick of the moment each day, and everyone wants to mitigate or minimize their financial and economic consequences. Knowingly or unknowingly, we do indeed heavily rely on the many works of actuaries.

Actuarial research today has gone into very diverse direction and in some sense, it is expanding the scope of actuarial work. It is the right moment to bring together the fine works of several strong and active scholars and researchers with the hope that research in the discipline stays on the right direction. It is also the aim of this workshop that through such discussion and exchange of ideas, future collaborations may effectively prosper within the discipline. We have identified five (5) key areas of research topics to be discussed in this workshop:

1. Risk and loss model construction: It has been considered conventional in actuarial science to construct mathematical models, use historical data to calibrate and estimate these models, and implement them as predictive models. These predictive models provide tools for actuaries to better assess future risks and losses. By the very nature of its importance, predictive models are increasingly becoming popular today in both theoretical research and practice.

2. Interface between actuarial mathematics and statistical sciences: Rapid advances in the statistics discipline are helping to contribute to its increasing applications in many other disciplines. Today, we find a broad spectrum of statistical tools for data analysis and interpretation in medicine, engineering, environmental sciences, to name a few. Actuarial science is no exception here; we rely on many tools and techniques in the statistical sciences and there has been success in applying these tools such as the recent use of copulas for understanding dependencies and constructing multivariate models. Statistics is ever becoming more widespread in actuarial science as micro-level data becomes more available for model calibration, and technology is making it manageable to acquire and analyze these data.

3. Convergence between actuarial and financial mathematics: There is an explosion of financial products in the marketplace that combine the characteristics of investment and actuarial risks. To many, this phenomenon is contributing to the growth of a number of so-called actuaries of the third kind. Insurance products are now becoming more complex to price and companies are continuing to look at the financial market for investors who may be willing to assume excess in actuarial risks. A clear example is the recent development of mortality derivative and longevity bond products as a result of increased longevity risks to insurers. Such product innovations, called insurance-linked securities, are creating exchanges of tools used in both actuarial and financial mathematics.

4. Risk measurement and management: Identification is a preliminary process in the measurement and management of risks. The advances in the quantitative methods of risk measurement is now going beyond learning methods to manage these risks. There are clear overlaps and extensions of this topic with loss models, use of more sophisticated statistical methods and use of financial and investment theory.

5. The bridge between theory and practice: The value of actuarial research will continue to be assessed on how rapid practitioners will learn and implement them into practice. Recently there has been a global movement to regulate insurance and similar financial institutions to assist companies stay solvent for the benefit of consumers and the marketplace as a whole. In Europe, for example, the Solvency II and the Basel Accords are directives being formally implemented to regulate solvency of insurance companies and banks. For example, similar directives in Canada have been for years implemented with the federal Office of the Superintendent of Financial Institutions (OSFI) taking a lead role in solvency regulation. These are examples where theory and practice have come to interplay to attempt to develop a sound regulatory framework for solvency. We wish to continue this kind of collaboration and communication between theoreticians and industry practitioners.

Actuarial science developed in the 16th century when Edmond Halley, then a famous mathematician, constructed a mortality table and described the work in a research paper on how to use such table to price annuities and insurance. This paper is considered one of the early pioneers of the discipline that has evolved some 300 years ago, yet even in the last century alone, many famous mathematicians who also considered themselves as actuaries have made major contributions in the foundation of probability and statistics. Three of them are worth mentioning here: Lundberg (1876-1965), Cramer (1893-1985) and deFinetti (1906-1985). Today, research in the discipline is continuing to evolve applying even more advanced mathematical concepts and constructs partly influenced by several factors that are directly affecting our everyday lives. To illustrate for example, almost generally everywhere, we continue to find strong evidence of people living longer, having now to expect longer retirement period and increasingly be concerned of outliving economic resources. The increase in volatility in the financial market is shaping up changes in the features and returns of many investment products. Erratic changes in climate are contributing to a deluge of uncertainty about natural catastrophes such as hurricanes and floods.

On a worldwide basis, we are experiencing a very rapid growth in actuarial research which in some sense, is driven by multiple forces. There is an increase in demand for actuarial skills in the financial sector that is contributing to the growing number of actuarial programs being offered at various colleges and universities. As a result, actuarial educators are in huge demand creating a growth in the number of researchers in the field. The actuarial discipline is continuing to evolve because the role of actuarial science to manage financial security programs is rapidly expanding beyond the tradition of just calculating premiums or contributions needed to fund such programs like insurance and pensions. Investment risk is increasingly becoming volatile; natural catastrophes are contributing to an increasing dangerous world we live in. There is a rapid growth in sophisticated modeling taking place in related fields such as statistics, finance and even medical science that are also impacting the essence of actuarial work.

The actuarial profession is also gaining popularity recently for many good reasons: we are learning so much more on how the science is affecting our lives and actuaries have year after year been recognized as holding one of the top jobs in Canada, the US and many elsewhere globally. It is therefore the right time to evaluate the direction of research in this discipline. This workshop aims to discuss recent advances in research in actuarial mathematics, so that the right direction can be assessed.