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Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization

Soňa Kilianová, Daniel Ševčovič (2018)

Kybernetika

In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation ( C V a R D ) based Sharpe ratio for measuring...

Exponentially long time stability for non-linearizable analytic germs of ( ℂ n , 0 ) .

Timoteo Carletti (2004)

Annales de l’institut Fourier

We study the Siegel-Schröder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey- s , s > 0 category. We introduce a new arithmetical condition of Bruno type on the linear part of the given germ, which ensures the existence of a Gevrey- s formal linearization. We use this fact to prove the effective stability, i.e. stability for finite but long time, of neighborhoods of the origin, for the analytic germ.

Generalized Hamiltonian dynamics after Dirac and Tulczyjew

Fiorella Barone, Renato Grassini (2003)

Banach Center Publications

Dirac's generalized Hamiltonian dynamics is given an accurate geometric formulation as an implicit differential equation and is compared with Tulczyjew's formulation of dynamics. From the comparison it follows that Dirac's equation-unlike Tulczyjew's-fails to give a complete picture of the real laws of classical and relativistic dynamics.

Generic Nekhoroshev theory without small divisors

Abed Bounemoura, Laurent Niederman (2012)

Annales de l’institut Fourier

In this article, we present a new approach of Nekhoroshev’s theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak, it combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of...

Geometric mechanics on nonholonomic submanifolds

Olga Krupková (2010)

Communications in Mathematics

In this survey article, nonholonomic mechanics is presented as a part of geometric mechanics. We follow a geometric setting where the constraint manifold is a submanifold in a jet bundle, and a nonholonomic system is modelled as an exterior differential system on the constraint manifold. The approach admits to apply coordinate independent methods, and is not limited to Lagrangian systems under linear constraints. The new methods apply to general (possibly nonconservative) mechanical systems subject...

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