Hedging of contingent claims under incomplete information. (English) Zbl 0738.90007

Applied stochastic analysis, Pap. Workshop, London/UK 1989, Stochastic Monogr. 5, 389-414 (1990).
[For the entire collection see Zbl 0728.00017.]
We consider an incomplete market and want to find optimal hedging strategies for contingent claims when the underlying price process \(X\) is a continuous semimartingale. A first solution is provided by a martingale projection argument with respect to the minimal equivalent martingale measure \(\hat P\) for \(X\). We introduce this notion, discuss existence and uniqueness of \(\hat P\) and give a characterization in terms of a relative entropy. If \(X\) is complete under a larger filtration, we can also obtain the optimal strategies under certain assumptions by a projection onto the given smaller filtration. As an example of the second type, we study the case where \(X\) is a diffusion with a random variance.
Reviewer: H.Föllmer


91G20 Derivative securities (option pricing, hedging, etc.)
60J60 Diffusion processes
91B24 Microeconomic theory (price theory and economic markets)


Zbl 0728.00017