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Theses

Problèmes de contrôle stochastiques : contrôle sous contrainte, contrôlabilité et application à la réassurance

Abstract : The aim of this thesis is to present some contributions in the framework of control for stochastic differential equations in finite or infinite dimension:
(1) Non-compact-valued stochastic control under state constraints;
The first chapter is devoted to the study of a necessary condition under which the solutions of a stochastic differential equation governed by unbounded control processes remain in an arbitrarily small neighborhood of a given set of constraints.
(2) Approximate controllability for linear SDEs with control acting on the noise;
In this chapter we study approximate controllability for a linear SDE for the case when the control acts also on the noise. We prove, using the dual BSDE and Riccati methods that approximate controllability is equivalent to the local in time viability for a suitable set.
(3) Approximate Controllability for Linear Stochastic Differential Equations in Infinite Dimensions ;
We investigate the approximate controllability property of a stochastic linear system on a separable real Hilbert space. In particular, we prove the existence and uniqueness for the (dual) linear BSDE with linear unbounded operators acting on Y and on Z and we show the duality between approximate controllability and observability.
(4) Insurance, Reinsurance and Dividend Payment;
The aim of this chapter is to introduce an insurance model allowing reinsurance and dividend payment. Our model deals with several homogeneous contracts and takes into account the legislation regarding the provisions to be justified by the insurance companies.
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https://tel.archives-ouvertes.fr/tel-00258044
Contributor : Dan Goreac <>
Submitted on : Thursday, February 21, 2008 - 12:40:04 AM
Last modification on : Wednesday, October 14, 2020 - 3:52:16 AM
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Dan Goreac. Problèmes de contrôle stochastiques : contrôle sous contrainte, contrôlabilité et application à la réassurance. Mathématiques [math]. Université de Bretagne occidentale - Brest, 2007. Français. ⟨tel-00258044⟩

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