Saddle-Point Structures for Two-Player Zero-Sum SDEs with Lévy Noise
Existence, coincidence of values, and a non-local first-order condition
We extend the standard zero-sum stochastic differential game to a state process driven by a Lévy noise. Under the operator register established in the institute’s resolvent paper, the upper and lower value functions exist, are 1/2-Hölder, and coincide as viscosity solutions of the Hamilton-Jacobi-Isaacs integro-differential equation. The saddle-point strategy pair is characterised by a non-local first-order condition, and a worked example — a central-bank-versus-speculator drift-and-intensity game — illustrates the construction with a closed-form saddle.