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Research Seminar Series in Statistics and Mathematics

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

Type Lecture / discussion
SpeakerCosimo-Andrea Munari (Department of Banking and Finance, University of Zurich)
Organizer Institut für Statistik und Mathematik

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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