Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems

Homotopy for Rational Riccati Equations Arising in Stochastic Control

We consider the numerical solution of the rational algebraic Riccati equations in Rn, arising from stochastic optimal control in continuousand discrete-time. Applying the homotopy method, we continue from the maximal stabilizing solutions of the deterministic algebraic Riccati equations, which are readily available. The associated differential equations require the solutions of some generalized...

Generalized Riccati Equations Arising in Stochastic Games

We study a class of rational matrix differential equations that generalize the Riccati differential equations. The generalization involves replacing positive definite “weighting” matrices in the usual Riccati equations with either semidefinite or indefinite matrices that arise in linear quadratic control problems and differential games−both stochastic and deterministic. The purpose of this pape...

Optimal Control Problems of Forward-Backward Stochastic Volterra Integral Equations with Closed Control Regions

Abstract. Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs, in short) with closed control regions are formulated and studied. Instead of using spike variation method as one may imagine, here we turn to treat the non-convexity of the control regions by borrowing some tools in set-valued analysis and adapting them into our stochastic control systems. A ...

Some Problems in Nonlinear Volterra Integral Equations

Upper and lower bounds for the norm of solutions of systems of first order differential equations as well as theorems on global existence and boundedness and other useful results have recently been obtained by comparing solutions of the given system with those of a related (single) first order differential equation. This technique, which is essentially due to Conti [5] and Wintner [9], has been...

Stochastic Volterra integral equations with a parameter