Department of

Mathematics


Seminar Calendar
for Actuarial Science events the next 12 months of Friday, January 1, 2016.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, March 15, 2016

4:00 pm in Altgeld Hall 159,Tuesday, March 15, 2016

Analytic Solution for Ratchet Guaranteed Minimum Death Benefit Options Under a Variety of Mortality Laws

Eric Ulm (Georgia State University)

Abstract: We derive a number of analytic results for GMDB ratchet options. Closed form solutions are found for De Moivreís Law, Constant Force of Mortality, Constant Force of Mortality with an endowment age and constant force of mortality with a cutoff age. We find an infinite series solution for a general mortality laws and we derive the conditions under which this series terminates. We sum this series for at-the-money options under the realistic Makehamís Law of Mortality.

Tuesday, September 20, 2016

4:00 pm in 1 Illini Hall,Tuesday, September 20, 2016

Coherent mortality forecasts for dependent populations: a Bayesian approach

Anastasios Bardoutsos (University of Groningen)

Abstract: Underestimating the future improvement of mortality rates translates into higher than expected pay-out-ratios for pensions funds and insurance companies and therefore implies a risk, the so-called longevity risk. The solvency of pension systems and annuity providers in the presence of longevity risk is a major point of concern. Quantification of the longevity risk with appropriate stochastic mortality models is key. Recent studies propose multi-population stochastic mortality models as a strategy for achieving robust and coherent projections of mortality rates. This paper presents a Bayesian analysis of two coherent multi-population models of log-bilinear type, designed for two or more populations, while allowing for dependence between these populations. The first model is inspired by Cairns et al. (2011) and Enchev et al. (2016), and the second is the well known Li & Lee model, proposed by Li and Lee (2005). For both models we identify the parameters through appropriate constraints and we avoid the multi-step calibration strategy that is currently used in the literature. We assume a Poisson distribution for the number of deaths at a certain age and in a certain period and include full dependency between the period effects. As such, we extend earlier work where period effects are considered independent. Moreover, we utilize the Kannisto parametric mortality law to close the generated mortality scenarios for higher ages and provide projections of important demographic markers, such as period and cohort life expectancy. We develop the technicalities necessary for Markov Chain Monte Carlo ([MCMC]) simulations and provide software implementation (in R) for the models discussed in the paper. We finally present a case study using five European countries which are geographically close and share similar socio-economic characteristics.

Tuesday, November 1, 2016

4:00 pm in 1 Illini Hall,Tuesday, November 1, 2016

Stable Risk Sharing and Its Monotonicity

Xin Chen (Industrial and Enterprise Systems Engineering, UIUC)

Abstract: We consider a risk sharing problem in which agents pool their random costs together and seek an allocation rule to redistribute the risk back to each agent. The problem is put into a cooperative game framework and we focus on two salient properties of an allocation rule: stability and monotonicity employing concepts of core and population monotonicity from cooperative game theory. When the risks of the agents are measured by coherent risk measures, we construct a risk allocation rule based on duality theory and establish its stability. When restricting the risk measures to the class of distortion risk measures, the duality-based risk allocation rule is population monotonic if the random costs are independent and log-concave. For the case with dependent normally distributed random costs, a simple condition on the dependence structure is identified to ensure the monotonicity property.

Tuesday, November 8, 2016

4:00 pm in 314 Altgeld Hall,Tuesday, November 8, 2016

Applications of Predictive Analytics: Improving Business Operations for Life Insurance Companies

Andy Ferris, FSA, MAAA, CFA (Managing Director at Deloitte Consulting)

Abstract: Why is the SOA adding a predictive analytics component to the ASA curriculum? Join Andy Ferris to hear about predictive analytics in practice. Ferris will discuss how his teams are deploying applications of predictive analytics to disrupt and improve core life insurance company operations. He'll present several examples of "traditional" business processes at life insurance companies and how those processes can be re-designed with applications of predictive analytics to save time, save money, and to deliver a better customer experience. He'll share his insights on the role of the actuary as "the engineer of a life insurance company" in introducing applications of predictive analytics in core business operations. Ferris will also explain how the changes in the ASA curriculum will ensure that all students going forward have a fundamental understanding of predictive analytics.

Tuesday, November 15, 2016

4:00 pm in 445 Altgeld Hall,Tuesday, November 15, 2016

A Theory for Measures of Tail Risk

Dr. Fangda Liu (Central University of Finance and Economics, China)

Abstract: In modern risk management, a crucial consideration is how to describe and quantify a risk according to its tail behaviour. Prominent, yet elementary, examples of tail risk measures are Value-at-Risk (VaR) and the Expected Shortfall (ES), which are two popular classes of regulatory risk measures in banking and insurance. To achieve a comprehensive understanding of the tail risk, we carry out an axiomatic study for risk measures which quantify the tail risk, that is, the behavior of a risk beyond a certain quantile. We establish a connecting between a tai risk measure and its generator, and investigate their joint properties. A tail risk measure inherits many properties from its generator, but not subadditivity or convexity; nevertheless, a tail risk measure is coherent if and only if its generator is coherent. We explore further tail shortfall risk measure and elicitability. In particular, there is no elicitable tail convex risk measure rather than the essential supremum, and under a continuity condition, the only elicitable and positively homogeneous monetary tail risk measures are the VaRs.