BEGIN:VCALENDAR
PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20230428T121219Z
DTSTART:20230503T110000Z
DTEND:20230503T120000Z
SUMMARY:Abigail Mellor - Asymptotic analysis and efficient numerical solu
tion of the Fokker-Planck Equations (with application to derivatives pri
cing)
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}j1d2-lgkwcy
y4-n9hska
DESCRIPTION:Abigail Mellor (University of Manchester) will speak in the P
robability seminar. (in-person)\n\nThe Fokker-Planck Equations (FPEs) ar
e ubiquitous in numerous disciplines\, not least in financial mathematic
s\, where a popular technique for pricing derivatives is enabled through
the derivation of the density function via the FPE governing its evolut
ion. Accuracy and efficiency are both keys in derivatives pricing\, but
satisfying both is a challenge due to the delicate mathematical structur
e often encountered. Our work currently focuses on pricing derivatives w
ith one and two assets following generalised Ornstein-Uhlenbeck processe
s. In such scenarios\, the elasticity of variance parameter(s) of the pr
ocess(es) may induce a degenerate region at the origin (for instance\, w
hen this parameter is fractional). Here\, the solution structure can be
intricate\, and standard computational methods fail as they violate the
necessary â€˜particle-conservingâ€™ condition. We present rigorous asymptoti
c analyses to shed light on the aforementioned intricate/singular mathem
atical structures which render standard numerical techniques unfeasible.
By incorporating these structures into our numerical schemes\, while en
suring that the particle-conservation condition is fully satisfied\, we
obtain robust numerical solutions (as confirmed by extensive numerical-s
cheme experimentation) with modest computational facilities.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Maurice Priestley Room G.108\, Alan Turing Building\, Manchester
END:VEVENT
END:VCALENDAR