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!