Department of

Mathematics


Seminar Calendar
for Actuarial Science events the next 12 months of Sunday, January 1, 2017.

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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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Wednesday, January 25, 2017

4:00 pm in 245 Altgeld Hall,Wednesday, January 25, 2017

Degenerate diffusions and heat kernel estimates

Jing Wang (J.L. Doob Research Assistant Professor, University of Illinois at Urbana-Champaign)

Abstract: In this talk we will look at degenerate hypoelliptic diffusion processes and the small time behaviors of their transition densities. Diffusion processes play important roles in modeling risky assets in financial mathematics and actuarial science. The small time estimates of their transition densities are particularly useful for pricing options with short maturities. In this talk we will introduce the degenerate diffusion processes that are characterized by their levels of degeneracy. The ones of weaker degeneracy -- also called strong Hörmander's type -- are closely related to sub-Riemannian geometry. An important example is the Brownian motion process on a sub-Riemannian manifold. In general, small time asymptotic estimates are available for a subelliptic heat kernel on the diagonal and out of cut-locus. In special cases such as for Brownian motions on sub-Riemannian model spaces, we can obtain explicit expressions for their transition densities (heat kernels) and hence small time asymptotic estimates, particularly on the cut-loci. In the second part of the talk, we will study the strictly degenerate case-diffusion processes that are of weak Hörmander's type. Namely the hypoellipticity is fulfilled with the help of the drift term. This type of processes are particularly interesting in financial mathematics for pricing Asian options. We obtain large deviation properties for nilpotent diffusion processes of weak Hörmander's type.

Monday, January 30, 2017

4:00 pm in 156 Henry Admin Bldg,Monday, January 30, 2017

Discounted Sums at Renewal Times

Daniel Dufresne (Director of the Centre for Actuarial Science, University of Melbourne)

Abstract: Actuarial models usually include discounting, to take the time value of money into account. Mathematically this has proved difficult when amounts are paid at random times, for instance in risk theory. We assume that i.i.d. amounts {C(k)} are paid at renewal times {T(k)}. Of practical interest is the distribution of Z(t), the discounted value of claims occurring over the period [0,t]. New results on how to find the distribution of Z(t) will be presented. An important tool is sampling the process {Z(t)} at an independent exponential time, which leads to explicit distributions of Z(t) in specific cases. Joint work with Zhehao Zhang.

Monday, April 10, 2017

6:00 pm in 1092 Lincoln Hall,Monday, April 10, 2017

Success in Your Actuarial Career

Brian Brown, FCAS, MAAA (Principal, Consulting Actuary, Milliman)

Abstract: Brian is a principal and consulting actuary with the Chicago office of Milliman. He joined the firm in 1990. He serves as Milliman Global Practice Director, Casualty, and is President-Elect of the Casualty Actuarial Society. Brian’s area of expertise is property and casualty insurance, especially ratemaking, loss reserve analysis, and actuarial appraisals for mergers and acquisitions. Brian has extensive experience in both commercial and personal lines, including professional liability and workers’ compensation. He has also provided legal support services to law firms.Brian’s clients include many of the largest insurers/reinsurers in the world. He is a Fellow, Casualty Actuarial Society, and a member of the American Academy of Actuaries. He received his BS in Economics from Illinois State University.

Wednesday, September 6, 2017

3:00 pm in 345 Altgeld Hall,Wednesday, September 6, 2017

Modeling Dependent Insurance Risks: Customer Loyalty and Risk in Personal Insurance

Edward W. Frees (University of Wisconsin-Madison, Risk and Insurance)

Abstract: In the first portion of the talk I discuss the importance of modeling dependencies among insurance risks. I set the stage for this by describing various risk control mechanisms that the insurer has at its disposal and use this platform for describing the types of associations that are of concern to insurers. To model dependencies, I focus on the use of a copula, a probabilistic tool widely used in insurance and other disciplines. The second portion of the talk, on "Customer Loyalty and Risk in Personal Insurance," is joint work with Catalina Bolancé, Montserrat Guillén, and Emiliano Valdez. This work connects two strands of research on modeling personal (automobile and homeowners) insurance. One strand involves understanding the joint outcomes of separate personal insurance contracts, e.g., do higher automobile claims suggest more severe homeowner claims? A second strand of the literature involves understanding determinants of customer loyalty. For example, we now know that when a customer cancels one insurance contract, he or she is likely to cancel all other contracts soon after. We use copula regression to model the joint outcomes of auto and home claims as well as customer loyalty. Including customer loyalty, or duration with the company, is complicated because of the censoring of this time variable as well as the discreteness. Although customers may cancel the contract at any time, cancellation typically occurs at contract renewal, making this variable essentially a discrete outcome. Composite likelihood and generalized method of moments techniques allow us to address the special features of this data structure.

Tuesday, September 12, 2017

3:00 pm in 345 Altgeld Hall,Tuesday, September 12, 2017

Asymptotic theory of parametric inference for ruin probability under Levy insurance risks

Yasutaka Shimizu (Department of Applied Mathematics, Waseda University)

Abstract: The aim of this paper is to construct the confidence interval of the ultimate ruin probability under the insurance surplus driven by a Levy process. Assuming a parametric family for the Levy measures, we estimate the parameter from the surplus data, and estimate the ruin probability via the "delta method". However the asymptotic variance includes the derivative of the ruin probability with respect to the parameter, which is not generally given explicitly, and the confidence interval is not straightforward even if the ruin probability is well estimated. This paper gives the Cramer-type approximation for the derivative, and gives an asymptotic confidence interval of ruin probability.

Tuesday, October 3, 2017

3:00 pm in 345 Altgeld Hall,Tuesday, October 3, 2017

Valuation of Large Variable Annuity Portfolios: Challenges and Potential Solutions

Guojin Gan (Department of Mathematics, University of Connecticut)

Abstract: In the past two decades, lots of variable annuity contracts have been sold by insurance companies. Insurers with large blocks of variable annuity business have faced great challenges especially when it comes to valuing the complex guarantees embedded in these products. The financial risks associated with guarantees embedded in variable annuities cannot be adequately addressed by traditional actuarial approaches. In practice, dynamic hedging is usually adopted by insurers and the hedging is done on the whole portfolio of VA contracts. Since the guarantees embedded in VA contracts sold by insurance companies are complex, insurers resort to Monte Carlo simulation to calculate the Greeks required by dynamic hedging but this method is extremely time-consuming when applied to a large portfolio of VA contracts. In this talk, I will talk about two major computational problems associated with dynamic hedging and present some potential solutions based on statistical learning to address these computational problems.

Friday, October 20, 2017

8:00 am in TBA,Friday, October 20, 2017

Tuesday, November 7, 2017

3:00 pm in 345 Altgeld Hall,Tuesday, November 7, 2017

To Be Announced

Zhongyi Yuan (Pennsylvania State University Smeal College of Business)

6:30 pm in 1320 DCL,Tuesday, November 7, 2017

The SOA Curriculum Changes

Stuart Klugman, FSA, CERA, PhD (SOA Senior Staff Fellow, Education)

Abstract: With a unique perspective on the exams and modules, Stuart will discuss changes to the SOA curriculum. Stuart Klugman (FSA, CERA, PhD) is a Senior Staff Fellow in the Education Department at the SOA, a position he has held since 2009. From 1974-2009 he was a professor at The University of Iowa and Drake University, retiring from Drake as the Principal Financial Group Distinguished Professor of Actuarial Science. He has co-authored/edited three books used on SOA exams, published numerous research papers, and served two terms on the SOA Board of Directors. He co-chaired the committee that developed the 2005-2007 exam changes and provided staff support for the 2018 changes. He is a two-time recipient of the SOA’s Presidential Award.