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In this way the fifth order compatibility partial differential equation in terms of stream functions can readily be written by two coupled fifth order ordinary differential equations. Technical appendices present analyses based on calculus, stochastics, and linear algebra; and introduce PDE2D, a general purpose partial differential equation solver. Dropping the subscripts to f, we deduce that any defaultable bond whose price, f, is contingent on the default-adjusted interest rate, R, the hazard rate, h, and time, t, satisfies the second-order partial differential equation |
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