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 I. Basic math.
 II. Pricing and Hedging.
 1 Basics of derivative pricing I.
 2 Change of numeraire.
 3 Basics of derivative pricing II.
 4 Market model.
 5 Currency Exchange.
 6 Credit risk.
 7 Incomplete markets.
 A. Single time period discrete price incomplete market.
 B. Coherent measure.
 C. Incomplete market with multiple participants.
 D. Example: uncertain local volatility.
 III. Explicit techniques.
 IV. Data Analysis.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 VIII. Bibliography
 Notation. Index. Contents.

## Incomplete market with multiple participants.

e hinted on several occasions that model-consistent pricing of large variety of financial instruments is neither possible nor necessary. However, one still needs to install consistent hedges. In this section we describe an intuitive technique for calculation of such hedges. The presentation is based on [Cherny2006] .

We are working in the setup described by ( Finite space variable incomplete market ). However, we assume that there are several participants on the market (or several trading desks participating in a structured trade) using the sets of valuation measures with the index being the participant index and being the model index. The trade is an acceptable opportunity if it may be represented as sum with each component being acceptable in the sense of the previous section and with respect to .

We already remarked in the previous section that the pricing technique of the formulas ( Incomplete market ask ),( Incomplete market bid ) represent the coherent measure pricing. The coherent measure ( Coherent measure ) may be regarded as the support function ( Support function ). It remains to point out that we operate in the situation of the infimal convolution ( Infimal convolution ). We combine the results ( Existence of incomplete market pricing ),( Incomplete market ask ),( Incomplete market bid ) and the result ( Infimal convolution of support functions ) and arrive to the version of the statement ( Incomplete market ask ),( Incomplete market bid ) with replaced for .

 Notation. Index. Contents.