Monotone and Cash-Invariant Convex Functions and Hulls
Damir Filipović(joint with Michael Kupper)
University of Munichwww.math.lmu.de/~filipo
Advances in Mathematics of FinanceSecond General AMaMeF Conference and
Banach Center ConferenceBedlewo, Poland, 2 May 2007
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Overview
• Motivating examples
• Convex monotone cash-invariant functions
• Monotone and cash-invariant hulls
• Examples
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0 21
1
t
1-p
p
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Program
Characterize convex monotone functions
Characterize convex cash-invariant functions
Construct monotone and cash-invariant hulls
What can we learn from it?Construct new and rediscover old convex risk
measures
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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!