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DTSTART;TZID=America/Los_Angeles:20191014T161500
DTEND;TZID=America/Los_Angeles:20191014T171500
DTSTAMP:20260425T203312
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SUMMARY:Applied Math Talk: A Full Asymptotic Series of European Call Option Prices in the SABR Model with Beta = 1 given by Zhengji Guo (CGU)
DESCRIPTION:We develop two new pricing formulae for European options. The purpose of these formulae is to better understand the impact of each term of the model\, as well as improve the speed of the calculations. We consider the SABR model (with $\beta=1$) of stochastic volatility\, which we analyze by tools from Malliavin Calculus. We follow the approach of Alòs et al (2006) who showed that under stochastic volatility framework\, the option prices can be written as the sum of the classic Hull-White (1987) term and a correction due to correlation. We derive the Hull-White term\, by using the conditional density of the average volatility\, and write it as a two-dimensional integral. For the correction part\, we use two different approaches. Both approaches rely on the pairing of the exponential formula developed by Jin\, Peng\, and Schellhorn (2016) with analytical calculations. The first approach\, which we call ”Dyson series on the return’s idiosyncratic noise” yields a complete series expansion but necessitates the calculation of a 7-dimensional integral. Two of these dimensions come from the use of Yor’s (1992) formula for the joint density of a Brownian motion and the time-integral of geometric Brownian motion. The second approach\, which we call ”Dyson series on the common noise” necessitates the calculation of only a one-dimensional integral\, but the formula is more complex. This research consisted of both analytical derivations and numerical calculations. The latter show that our formulae are in general more exact\, yet more time-consuming to calculate\, than the first order expansion of Hagan et al (2002).
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-given-by-zhengji-guo-cgu/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Applied Math Seminar
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DTSTART;TZID=America/Los_Angeles:20191015T121500
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CREATED:20190830T203403Z
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SUMMARY:Sporadic points on modular curves (Ozlem Ejder\, Colorado State University)
DESCRIPTION:A classic and fundamental result in number theory is due to Mordell who proved that the set of points on an elliptic curve defined over a number field forms a finitely generated abelian group; in particular\, it has a finite torsion subgroup. An essential tool to study elliptic curves is the modular curves which are moduli spaces for elliptic curves with an additional structure.  In particular\, $X_1(n)$ classifies the elliptic curves with a point of order of $n$.  Motivated by the classification of torsion problems\, we study the sporadic points on the curve $X_1(n)$\, that is\, the closed points on $X_1(n)$ such that there are at most finitely many points of degree at most $\deg(x)$. In this talk\, we will discuss the finiteness of sporadic points. This is joint with A. Bourdon\, Y. Liu\, F. Odumudu and B. Viray.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-ozlem-ejder-colorado-state-university/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20191016T161500
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CREATED:20190826T234917Z
LAST-MODIFIED:20191007T175651Z
UID:1394-1571242500-1571246100@colleges.claremont.edu
SUMMARY:Habitat-driven extinctions: insights from spatially implicit ODE models 
DESCRIPTION:Speaker:  Kate Meyer\, Cornell University\n\n\n\n\n\n\n\n\n\nAbstract: Biodiversity underpins ecosystem functioning but continues to decline on a global scale. Among human activities driving this trend\, habitat destruction is a leading culprit in local and global extinctions. Simple mathematical models can address important questions surrounding habitat-driven extinctions—for example\, which species are at highest risk\, how delayed might extinction be\, and what can be done about it? Exploring these questions in a spatially implicit ODE model leads us to new mathematical territory involving temporary parameter changes and nonequilibrium dynamics.\n\n\n\nHost: Jasper Weinburd (jweinburd@hmc.edu)
URL:https://colleges.claremont.edu/ccms/event/tba-8/
LOCATION:CA
CATEGORIES:Colloquium
ORGANIZER;CN="Blerta Shtylla":MAILTO:shtyllab@pomona.edu
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