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Towards Exact Nonextensive Solutions Of The American Style Options III: Hamiltonians, Thermodynamics & Gibbs-Bogoliubov Inequalities.

Fredrick Michael

posted on 15 September 2018

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We have recently reported on the issue of uncertainty of exercise inherent to the American style option. This uncertainty results in an inequality between the portfolio and its constituent option and assets (etc.). We have approached this from the point of view of a random boundary in time problem by Green's functions methods in I, and more recently in II as a generalization of the linear programming approach where equalization of the otherwise inequality of the portfolio relation problem is made by introducing a 'slack' function which we identify with the uncertainty of exercise.

In this letter we continue this second approach however from a combined portfolio Black-Scholes approach coupled with an information theoretic and equivalently (maximum) entropy of thermodynamics Hamiltonian superposition view, and the Gibbs-Bogoliubov inequality approach.