On the Convergence of the p-Optimal Martingale Measures to the Minimal Entropy Martingale Measure

Abstract

In an incomplete financial market where asset prices are continuous semimartingales, we establish the convergence of the p-optimal martingale measures to the minimal entropy martingale measure as p tends to 1. The result is achieved exploiting the theory of BMO-martingales and semimartingale backward equations.

Key Words:

• Contingent claim pricing
• Incomplete financial markets
• Minimal entropy martingale measure
• p-Optimal martingale measure
• Semimartingale backward equation

Mathematics Subject Classification:

• 91B28
• 60H30
• 90C39

5. ACKNOWLEDGMENT

The author is indebted to her Ph.D supervisor, Michael Mania, for suggesting the topic of the paper and for constant encouragement. Special thanks are also due to Revaz Tevzadze for helpful advice and to David Hobson for an interesting conversation.