Research Seminar Series in Statistics and Mathematics
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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