Integral operator Riccati equations arising in stochastic Volterra control problems.

Summary We establish existence and uniqueness for infinite dimensional Riccati equations taking values in the Banach space L 1 (µ ⊗ µ) for certain signed matrix measures µ which are not necessarily finite. Such equations can be seen as the infinite dimensional analogue of matrix Riccati equations and they appear in the Linear-Quadratic control theory of stochastic Volterra equations.