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

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, January 25, 2017

Mathematics Colloquium - Special Lecture 2016-2017
4:00 pm   in 245 Altgeld Hall,  Wednesday, January 25, 2017
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Jing Wang (J.L. Doob Research Assistant Professor, University of Illinois at Urbana-Champaign)
Degenerate diffusions and heat kernel estimates
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

Mathematics Colloquium - Special Lecture 2016-2017
4:00 pm   in 156 Henry Admin Bldg,  Monday, January 30, 2017
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Daniel Dufresne (Director of the Centre for Actuarial Science, University of Melbourne)
Discounted Sums at Renewal Times
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.