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Dear Colleagues,

I would like to bring to your attention my papers of 1995 - 2011 on my semilinear evolution equation for American contingent claims in the entire domain of the state variables as well as the related nonlinear pricing semigroup and multiplicative measure that might be of interest to you - please kindly see references [1] – [12] below.

I introduced the semilinear evolution equation for American contingent claims as well as the related nonlinear pricing semigroup and multiplicative measure in 1995 - please kindly see references [10] – [12] below.

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

Sincerely,

Valery Kholodnyi

References:

[1] V.A. Kholodnyi, *A Nonlinear Partial Differential Equation for American Options in the Entire Domain of the State Variable*, Journal of Nonlinear Analysis, 30 (8) (1997) 5059-5070.

[2] V.A. Kholodnyi, *A Semilinear Evolution Equation for General Derivative Contracts,* In J.F. Price, Editor, Derivatives and Financial Mathematics, Nova Science Publishers, Inc., Commack, New York, 1997, 119 –138.

[3] V.A. Kholodnyi, *Universal Contingent Claims and Multiplicative Measures: Examples and Applications*, Proceedings of the 4^{th} International Conference on Nonlinear Problems in Aviation and Aerospace, European Conference Publications, Cambridge, United Kingdom, 2003, 259-270.

[4] V.A. Kholodnyi, *Universal Contingent Claims in a General Market Environment and Multiplicative Measures*, Proceedings of the 4^{th} International Conference on Dynamical Systems and Applications, Dynamic Publishers, Atlanta, Georgia, 2005, 206-212.

[5] V.A. Kholodnyi, *Universal Contingent Claims in a General Market Environment and Multiplicative Measures: Examples and Applications*, Journal of Nonlinear Analysis, 62 (2005) 1437-1452.

[6] V.A. Kholodnyi, *The Semilinear Evolution Equation for Universal Contingent Claims: Examples and Applications*, In R.P Agarwal and K. Perera, Editors, Proceedings of the Conference on Differential and Difference Equations and Applications, Hindawi, New York, 2006, 519 -528.

[7] V. A. Kholodnyi, *Valuation Multiplicative Measures and Universal Contingent Claims in a General Market Environment*, In X. Liu and S. X. Yang, Editors, Proceedings of the International Workshop on Differential Equations and Dynamical Systems, No. 2, Watam Press, Watereloo, 2006, 399 - 412.

[8] V.A. Kholodnyi, *Universal Contingent Claims and Valuation Multiplicative Measures with Examples and Applications*, Journal of Nonlinear Analysis, 69 (3) (2008) 880-890.

[9] V.A. Kholodnyi, *The Semilinear Evolution Equation for Universal Contingent Claims in a General Market Environment with Examples and Applications*, In S. Sivasundaram, J. Vasundhara Devi, F.E. Udwadia, and I. Lasiecka, Editors, Advances in Dynamics and Control: Theory, Methods and Applications, Cambridge Scientific Publishers, Cambridge, UK, 2011, 107 - 121.

[10] V.A. Kholodnyi, *A Nonlinear Partial Differential Equation for American Options in the Entire Domain of the State Variable*, IES Preprint, 1995.

[11] V.A. Kholodnyi, *A Semilinear Evolution Equation for General Derivative Contracts*, IES Preprint, 1995.

[12] V.A. Kholodnyi, *A Semilinear Evolution Equation for Universal Contingent Claims*, IES Preprint, 1995.

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