Saddle-Point Structures for Two-Player Zero-Sum SDEs with Lévy Noise
Existence, coincidence of values, and a non-local first-order condition
Two-player zero-sum stochastic differential games whose state is driven by a Lévy process, studied through the integro-differential Hamilton-Jacobi-Isaacs equation. The talk presents five results: regularity of upper and lower value functions, coincidence under the Isaacs condition, a non-local first-order condition characterising the saddle pair, a closed-form saddle for a central-bank-versus-speculator drift-and-intensity game, and numerical verification via Howard policy iteration.
Takeaways
- zero-sum stochastic differential game
- Lévy noise
- Hamilton-Jacobi-Isaacs equation