For linear-rate master equations the generating function admits an exact composition-multiplier representation whose Taylor coefficients on any finite window are obtained from a closed lower-triangular ODE of size 2(N+1), independent of the truncation cap N; the same closure is combined with Strang–
Affine Diffusion Processes: Theory and Applications
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abstract
We revisit affine diffusion processes on general and on the canonical state space in particular. A detailed study of theoretic and applied aspects of this class of Markov processes is given. In particular, we derive admissibility conditions and provide a full proof of existence and uniqueness through stochastic invariance of the canonical state space. Existence of exponential moments and the full range of validity of the affine transform formula are established. This is applied to the pricing of bond and stock options, which is illustrated for the Vasicek, Cox-Ingersoll-Ross and Heston models.
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2026 1verdicts
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Solving linear-rate ODE hierarchies (like master equations) using closures and operator splitting
For linear-rate master equations the generating function admits an exact composition-multiplier representation whose Taylor coefficients on any finite window are obtained from a closed lower-triangular ODE of size 2(N+1), independent of the truncation cap N; the same closure is combined with Strang–