Kolmogorov Backward Equations with Singular Diffusion Matrices

Singer, Hermann GND

The Feynman-Kac formula is derived from the Kolmogorov formula by using a state extension, which permits the absorption of the potential term into the drift part of the backward equation. The resulting homogenous equation with singular diusion matrix can be solved by using importance sampling techniques based on a drift correction. The method is applied to the Cameron-Martin formula, the quantum mechanical linear oscillator and the pricing of arithmetic Asian options.

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Singer, Hermann: Kolmogorov Backward Equations with Singular Diffusion Matrices. Hagen 2019. FernUniversität in Hagen.

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