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Actuarial Science is a collection of methods addressing quantitative problems in the insurance industry. The main research questions are the following.

  • When pricing a life insurance or a similar contract, how do we model the duration of the policy? How do we adjust historic life tables for the current health conditions, work environment, crime rate in the neighborhood, state of the economy, etc. If the life insurance paradigm is applied to a house, a boat and such, how do we model climatic changes and maintenance practices in the area?

  • Is there a way of quantifying the lemon premium (or adverse selection)? An example of lemon premium: the fact that a client is applying for a health insurance by itself increases the likelihood of some unobserved, detrimental health conditions.

  • If the contract allows for recurring events (e.g. car insurance, health insurance), which stochastic process do they follow? What can we say about the time between two successive accidents? Can we build a model where the system learns from the past and the likelihood of the next accident is a function of previous occurrences?

  • When insuring financial services companies, how topical is the renewal theory, which studies stochastic processes that reset themselves periodically? Does the financial industry learn anything in the long run?

  • How do we model codependence of claim intensities (or severity of losses) over different insurance policies within the same class of policies? Are symmetric and asymmetric copulas as well as correlated intensity models flexible enough to capture "tail events", scenarios when there are too many or too few claims coming? What is the breakdown of the aggregate risk between the likelihood of an event and the amount payable given the event?

  • How do we model codependence of claims over different market sectors? Are there "catastrophic events" that can trigger massive payouts over the whole spectrum of businesses? How can we estimate their likelihood if they are so rare and there is so little information on them? Can historical data be trusted at all?

  • If the insurance contract stipulates regular premium payments by the client, with the premium being fixed or tied to a specific index, how do we price this annuity? How complex should the models get to price varying annuities where the payments are correlated with interest rates?

  • In pension funding, how do we model the dynamics of age and overall demographic profile? Can we forecast cashflows in both directions 30 years from now with any reasonable level of accuracy?

  • What is the overall risk profile of an insurance company? How does the company perform the value-at-risk calculation to know how much reserves to set aside? What is the probability of the company going under from the point of view of ruin theory? How can the company rebalance the exposure to different lines of business to maximize the reward-to-risk ratio?

  • If the risk of an insurance company is too big and it wants to repackage and resell some of its policies as a financial derivative, with covenants and features, what is the price of this derivative? Alternatively, what risks are associated with the derivative and what can we say about the overall risk profile of a reinsurance company which buys the derivative?
To answer the questions above, actuarial science relies on the following methods: deterministic adjustment of life tables, survival analysis, counting processes with stochastic intensity, Markov chains, epidemic models, multivariate analysis, extreme value theory, interest rate models, credit risk models, general theory of derivatives pricing, nonparametric and parametric estimation, time series analysis, modern methods of nonlinear regression and classification (data mining), stochastic optimization, mechanism design and general ideas from game theory, and so on. The knowledge of all these methods is important for a modern actuary, even though most of them have been invented outside the actuarial community.

The major challenge in actuarial science is capturing extreme events, where substantial losses may come from different segments of the market within a relatively short period of time. The key analytical tasks here are 1) estimating the probability of rare trigger events and 2) capturing the highly nonlinear dependency structure of losses from different insurance contracts in an environment where there are no trigger events but the overall well-being deteriorates substantially. So far the tasks have not been addressed satisfactorily, as the recent Great Recession experience shows.



Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., & Nesbitt, C. J. (1997). Actuarial Mathematics (2nd ed). Society of Actuaries. - A big reference, which goes from the simple to the complex.

Shang, H. (2006). Actuarial Science: Theory and Methodology. World Scientific Publishing, Singapore. - This one is more focused on modern methods of actuarial mathematics.

Ross, S. M. (2009). Introduction to Probability Models (10th ed). Academic Press.

Lee, E. T., & Wang, J. W. (2003). Statistical Methods for Survival Data Analysis (3rd ed). Wiley-Interscience, Hoboken, New Jersey.

Salvadori, G., De Michele, C., Kottegoda, N. T., & Rosso, R. (2007). Extremes in Nature: An Approach Using Copulas. Springer.

Embrechts, P., Klüppelberg, C., & Mikosch, T. (2011). Modelling Extremal Events for Insurance and Finance (Corr. ed). Springer-Verlag Berlin Heidelberg.

Duffie, D., & Singleton, K. (2003). Credit Risk: Pricing, Measurement, and Management. Princeton University Press.

Rausand, M. & Høyland, A. (2004). System Reliability Theory: Models, Statistical Methods, and Applications. Wiley-Interscience, Hoboken, New Jersey. - This reference complements survival analysis, actuarial science and credit risk books because much attention is spent on the non-linear mechanism in which the reliability of the whole system depends on the reliability of separate parts.