Monotone and Cash-Invariant Convex Functions and Hulls

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Monotone and Cash-Invariant Convex Functions and
Hulls

• Damir Filipovic
• (joint with Michael Kupper)
• University of Munich
• www.math.lmu.de/filipo
• Advances in Mathematics of Finance
• Second General AMaMeF Conference and
• Banach Center Conference
• Bedlewo, 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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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!