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Titlebook: Mathematical Control Theory and Finance; Andrey Sarychev,Albert Shiryaev,Maria do Rosário G Book 2008 Springer-Verlag Berlin Heidelberg 20

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Instalment Options: A Closed-Form Solution and the Limiting Case, as they allow the holder to prolong a Vanilla Call or Put option by paying instalments of a discrete payment plan. We derive a closed-form solution to the value of such an option in the Black-Scholes model and prove that the limiting case of an Instalment option with a continuous payment plan is eq
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Existence and Lipschitzian Regularity for Relaxed Minimizers, problems of optimal control (Theorem 1); to derive conditions for Lipschitzian regularity of trajectories corresponding to relaxed minimizers (Theorem 3). In passing, elaborating on the approach used in [10], we provide a condition for Lipschitzian regularity of non relaxed minimizers (Theorem 2).
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An Approximate Solution for Optimal Portfolio in Incomplete Markets,an approximate solution for the optimal portfolio. We take into account a set of assets and a set of state variables, all of them described by general diffusion processes. Finally, we supply an easy test for checking the goodness of the approximate result.
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Observability of Nonlinear Control Systems on Time Scales - Sufficient Conditions,f operators which in the continuous-time case coincides with Lie derivatives associated to the given system. Then it is shown that set of functions generated by this operator distinguishes states that are distinguishable. The proved sufficient condition for observability is classical, but it works n
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