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Quadratic hedging and meanvariance portfolio selection with random parameters in an incomplete market
 Math. Opers. Res., Vol 29, No
, 2004
"... in an incomplete market ..."
Maximum principle for forwardbackward doubly stochastic control systems and applications,” ESAIM: Control,Optimization and Calculus of Variations, vol
 COCV
, 2011
"... ar ..."
Existence of an Optimal Control for Stochastic Control Systems with Nonlinear Cost Functional
"... Abstract We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate convexity assumptions on the coefficients of the for ..."
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Abstract We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate convexity assumptions on the coefficients of the forward and the backward equations we prove the existence of an optimal control on a suitable reference stochastic system. The proof is based on an approximation of the stochastic control problem by a sequence of control problems with smooth coefficients, admitting an optimal feedback control. The quadruplet formed by this optimal feedback control and the associated solution of the forward and the backward equations is shown to converge in law, at least along a subsequence. The convexity assumptions on the coefficients then allow to construct from this limit an admissible control process which, on an appropriate reference stochastic system, is optimal for our stochastic control problem.
ftp ejde.math.txstate.edu (login: ftp) A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS ON THE SPACE OF SYMMETRIC MATRICES
"... Abstract. In the first part of this paper we analyze the properties of the evolution operators of linear differential equations generating a positive evolution and provide a set of conditions which characterize the exponential stability of the zero solution, which extend the classical theory of Lya ..."
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Abstract. In the first part of this paper we analyze the properties of the evolution operators of linear differential equations generating a positive evolution and provide a set of conditions which characterize the exponential stability of the zero solution, which extend the classical theory of Lyapunov. In the main part of this work we prove a monotonicity and a comparison theorem for the solutions of a class of timevarying rational matrix differential equations arising from stochastic control and derive existence and (in the periodic case) convergence results for the solutions. The results obtained are similar to those known for matrix Riccati differential equations. Moreover we provide necessary and sufficient conditions which guarantee the existence of some special solutions for the considered nonlinear differential equations as: maximal solution, stabilizing solution, minimal positive semidefinite solution. In particular it turns out that under the assumption that the underlying system satisfies adequate generalized stabilizability, detectability and definiteness conditions there exists a unique stabilizing solution. 1.
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"... class of nonlinear differential equations on the space of symmetric matrices ..."
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class of nonlinear differential equations on the space of symmetric matrices
Optimal Variational Principle for Backward Stochastic Control Systems Associated with Lévy Processes ∗
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