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Dear Colleagues,

I would like to bring to your attention my paper of 2001 on differential geometry on graphs with applications to the foreign exchange option symmetry in a multiple currency foreign exchange market that might be of interest to you:

[1] V.A. Kholodnyi and J.F. Price, *Foreign Exchange Option Symmetry and a Coordinate-Free Description of a Multiple Currency Market in Terms of Differential Geometry on Graphs,* Journal of Nonlinear Analysis, 47 (9) (2001) 5885-5896.

I introduced the notion of the differential geometry on graphs in 1995 in the following preprint:

[2] V.A. Kholodnyi, *Beliefs-Preferences Gauge Symmetry Group and Dynamic Replication of Contingent Claims in a General Market Environment*, IES Preprint, 1995.

The foreign exchange symmetry was introduced in 1996 in the following preprints:

[3] V.A. Kholodnyi and J.F. Price, *Foreign Exchange Option Symmetry in a General Market Environment*, IES Preprint, 1996.

[4] V.A. Kholodnyi and J.F. Price, *Foreign Exchange Option Symmetry in a Multiple Currency General Market Environment*, IES Preprint, 1996.

Please also find below the references to some of my related published books and papers that might be also of interest to you:

[5] V.A. Kholodnyi, *Beliefs-Preferences Gauge Symmetry Group and Replication of Contingent Claims in a General Market Environment*, IES Press, Research Triangle Park, North Carolina, 1998.

[6] V.A. Kholodnyi and J.F. Price, *Foreign Exchange Option Symmetry*, World Scientific, River Edge, New Jersey, 1998.

[7] V.A. Kholodnyi and J.F. Price, *Foundations of Foreign Exchange Option Symmetry*, IES Press, Research Triangle Park, North Carolina, 1998.

[8] V.A. Kholodnyi, *Valuation and Dynamic Replication of Contingent Claims in the Framework of the Beliefs-Preferences Gauge Symmetry,* European Physical Journal B, 27 (2) (2002) 229-238.

[9] V.A. Kholodnyi and J.F. Price, *Foreign Exchange Option Symmetry Based on Domestic-Foreign Payoff Invariance*, Proceedings of the IEEE/IAFE Conference on Computational Intelligence for Financial Engineering (CIFEr), New York, (1997), 164-170.

For further information about my related books and papers please find below the link to my Profile at the ResearchGate: http://www.researchgate.net/profile/Valery_Kholodnyi.

Please let me know if you might have questions or would like further information.

Sincerely,

Valery Kholodnyi

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