Research Seminar Series in Statistics and Mathematics

Wirtschaftsuniversität Wien, Departments 4 D4.4.00809:00 - 10:30

Art Vortrag/Diskussion
Vortragende/rCosimo-Andrea Munari (Department of Banking and Finance, University of Zurich)
Veranstalter Institut für Statistik und Mathematik
Kontakt katrin.artner@wu.ac.at

Cosi­mo-Andrea Munari (Depart­ment of Banking and Finance, Univer­sity of Zurich) about “Exis­tence, uniqueness and stabi­lity of optimal port­fo­lios of eligible assets”

The Insti­tute for Statis­tics and Mathe­ma­tics (Depart­ment of Finance, Accoun­ting and Statis­tics) cordi­ally invites ever­yone inte­rested to attend the talks in our Rese­arch Seminar Series, where inter­na­tio­nally renowned scho­lars from leading univer­si­ties present and discuss their (working) papers.

The list of talks for the summer term 2018 is avail­able via the follo­wing link:
Summer Term 2018


In a capital adequacy frame­work, risk measures are used to deter­mine the minimal amount of capital that a finan­cial insti­tu­tion has to raise and invest in a port­folio of pre-­spe­ci­fied eligible assets in order to pass a given capital adequacy test. From a capital effi­ci­ency perspec­tive, it is important to iden­tify the set of port­fo­lios of eligible assets that allow to pass the test by raising the least amount of capital. We study the exis­tence and uniqueness of such optimal port­fo­lios as well as their sensi­ti­vity to changes in the under­lying capital posi­tion. This natu­rally leads to inves­ti­ga­ting the conti­nuity proper­ties of the set-va­lued map asso­cia­ting to each capital posi­tion the corre­spon­ding set of optimal port­fo­lios. We pay special atten­tion to lower semi­con­ti­nuity, which is the key conti­nuity property from a finan­cial perspec­tive. This "stabi­lity" property is always satis­fied if the test is based on a poly­he­dral risk measure but it gene­rally fails once we depart from poly­he­dra­lity even when the refe­rence risk measure is convex. However, lower semi­con­ti­nuity can be often achieved if one if one is willing to focuses on port­fo­lios that are close to being optimal. Besides capital adequacy, our results have a variety of natural appli­ca­tions to pricing, hedging, and capital allo­ca­tion problems.
(This is joint work with Michel Baes and Pablo Koch-­Me­dina.)

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