We would like to cor­di­al­ly in­vi­te you to two talks in the Vi­en­na Se­mi­nar in Ma­the­ma­ti­cal Fi­nan­ce and Pro­ba­bi­li­ty (joint­ly or­ga­ni­zed with TU Wien and Uni­ver­si­ty of Vi­en­na), ta­king place at WU next Thurs­day:

Clau­dio Fon­ta­na(De­part­ment of Ma­the­ma­tics "Tul­lio Levi-​Civita", Uni­ver­si­ty of Pa­do­va)
Data-​driven Heath-​Jarrow-Morton mo­dels
Thurs­day, Ja­nuary 23, 2025, 15:30, WU Cam­pus, Buil­ding D4, Room D4.0.127

Abs­tract:
We de­ve­lop a data-​driven ver­si­on of Heath-​Jarrow-Morton mo­dels in the con­text of in­te­rest rate mo­de­ling. We con­sider mo­dels dri­ven by a li­ne­ar func­tio­nal of the yield curve, such as a fa­mi­ly of re­p­re­sen­ta­ti­ve for­ward rates, pos­si­bly aug­men­ted by a set of eco­no­mic fac­tors. The vo­la­ti­li­ty is pa­ra­me­teri­zed by a neural net­work, the pa­ra­me­ters of which are lear­ned by ca­li­bra­ti­on to past mar­ket yield cur­ves. This re­sults in a data-​driven arbitrage-​free model for the pre­dic­tion of yield cur­ves. Our setup al­lows for the pos­si­bi­li­ty of sche­du­led jumps, which can arise from mo­ne­ta­ry po­li­cy de­cis­i­ons. We il­lus­tra­te our deep lear­ning pro­ce­du­re by re­con­st­ruc­ting and fo­re­cas­ting the Euro area yield cur­ves. Based on joint work with Chris­ta Cu­chie­ro (Uni­ver­si­ty of Vi­en­na) and Ales­san­dro Gno­at­to (Uni­ver­si­ty of Ve­ro­na).

Dörte Kre­her(De­part­ment of Ma­the­ma­tics, Humboldt-​Universität zu Ber­lin)
On the sto­chastic po­rous me­di­um equa­ti­on with sti­cky re­flec­ted be­ha­vi­or
Thurs­day, Ja­nuary 23, 2025, 16:45, WU Cam­pus, Buil­ding D4, Room D4.0.127

Abs­tract:
In re­cent years, a va­rie­ty of SPDE mo­dels have been sug­gested as ma­cro­scopic mo­dels for limit order books. In such a con­text, it is de­si­ra­ble that the infinite-​dimensional sto­chastic sys­tem, which mo­dels the quan­ti­ty of pla­ced limit or­ders, re­mains non-​negative. Mo­reo­ver, if one also wants to in­clu­de il­li­qui­di­ty ef­fects in the model, the dy­na­mics should be able to spend a po­si­ti­ve amount of time at zero. This mo­ti­va­tes to look for SPDEs with sti­cky re­flec­ted be­ha­vi­or at zero, in which case the zero level set may have po­si­ti­ve Le­bes­gue me­a­su­re. In ge­ne­ral, the ana­ly­sis of sti­cky re­flec­ted dif­fu­si­ons is chal­len­ging due to the dis­con­ti­nui­ty of the dif­fu­si­on co­ef­fi­ci­ent and the so­journ co­ef­fi­ci­ent at the re­flec­tion bounda­ry. In this talk, I will show how non-​negative mar­tinga­le so­lu­ti­ons of a cer­tain SPDE, the sto­chastic po­rous me­di­um equa­ti­on, with sti­cky re­flec­ted be­ha­vi­or at zero can be con­st­ruc­ted. The con­st­ruc­tion fol­lows by the sto­chastic Faedo-​Galerkin me­thod and em­ploys an Aubin-​Lyons type in­ter­po­la­ti­on ar­gu­ment for Sobo­lev spaces with dif­fe­rent space-​time re­gu­la­ri­ty to de­ri­ve the re­qui­red mo­ment esti­ma­tes. The talk is based on joint work with B. Ham­bly and K. Sta­ro­voi­tovs.

For fur­ther in­for­ma­ti­on and the se­mi­nar sche­du­le, plea­se visit:
https://fam.tu­wien.ac.at/events/vs-​mfp/