Monotone and CashInvariant Convex Functions and Hulls Damir

Monotone and Cash-Invariant Convex Functions and Hulls Damir Filipović (joint with Michael Kupper) University of Munich www. math. lmu. de/~filipo Advances in Mathematics of Finance Second General AMa. Me. F Conference and Banach Center Conference Bedlewo, Poland, 2 May 2007 Damir Filipovic, LMU

Overview • Motivating examples • Convex monotone cash-invariant functions • Monotone and cash-invariant hulls • Examples 2 May 2007 Damir Filipovic, LMU 2

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Program Ø Characterize convex monotone functions Ø Characterize convex cash-invariant functions Ø Construct monotone and cash-invariant hulls Ø What can we learn from it? àConstruct new and rediscover old convex risk measures 2 May 2007 Damir Filipovic, LMU 6

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Conclusion • We found tractable ways to explicitly calculate monotone and cash-invariant hulls. → Fix defective risk measures → Construct new ones • Thanks! 2 May 2007 Damir Filipovic, LMU 18