arXiv subjects

Jannis R. Dause

Publications and source records attributed to Jannis R. Dause.

2 recordsLinked to original sources

arXiv2026

Duality for Stochastic Control with non-Markovian Random Coefficients

We develop novel duality methods for stochastic optimal control problems under two sources of randomness and non-Markovian random coefficients adapted to just one of them. The Hamilton-Jacobi-Bellman (HJB) equation is a second-order backward stochastic partial differential equation. Our duality theory provides an alternative description of the random value function in terms of a suitable pathwise optimal control problem parameterized by the realizations of one of the Brownian motions. This allows us to regain Markovianity using the theory of rough optimal control problems, leading to rough second order HJB equations that we solve in a suitable viscosity sense.

math.OC↗

arXiv2026

Controlled fields, rough stochastic calculus, and Itô-Wentzell-Alekseev-Gröbner identities

We develop a calculus of space-time controlled fields for rough stochastic systems. This approach provides a unified composition rule for evaluating random fields along rough semimartingales and yields a rough stochastic Itô-Wentzell formula under natural and verifiable regularity assumptions. Our motivation comes from works of Hudde et al. (2024) and, independently, Del Moral and Singh (2022) where the authors established, respectively, Itô-Alekseev-Gröbner, backward Itô-Wentzell, and diffusion interpolation formulas.

math.PR↗