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Optimal investment under stochastic volatility and power type utility function

Benchaabane, Abbes, Benchettah, Azzedine (2011)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20.In this work we will study a problem of optimal investment in financial markets with stochastic volatility with small parameter. We used the averaging method of Bogoliubov for limited development for the optimal strategies when the small parameter of the model tends to zero and the limit for the optimal strategy and demonstrated the convergence of these optimal strategies.

Optimal stability and instability results for a class of nearly integrable Hamiltonian systems

Massimiliano Berti, Luca Biasco, Philippe Bolle (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We consider nearly integrable, non-isochronous, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) O ⁢ µ -perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time T d = O ⁢ 1 / μ ⁢ log ⁡ 1 / μ by a variational method which does not require the existence of «transition chains of tori» provided by KAM theory. We also prove that our estimate of the diffusion time T d is optimal as a consequence of a general stability result proved via classical perturbation...

Optimisation of time-scheduled regimen for anti-cancer drug infusion

Claude Basdevant, Jean Clairambault, Francis Lévi (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control technique...

Optimisation of time-scheduled regimen for anti-cancer drug infusion

Claude Basdevant, Jean Clairambault, Francis Lévi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control...

Pointwise representation method.

Osipov, Vladimir Mihajlovich, Osipov, Vladimir Vladimirovich (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Polysystem Modelling of Geographical Processes and Phenomena in Nature and Society

A. K. Cherkashin (2009)

Mathematical Modelling of Natural Phenomena

Polysystem methodology elaborated for comprehensive analysis of geographical objects considers them as interrelated systems of different types. Each systematic interpretation of a territorial object is formed as a theory describing this object with a special language used for construction of a certain type of models. This paper proposes new methods to develop geographical models and describes several types of systematic models constructed by these methods.

Population Dynamics of Grayling: Modelling Temperature and Discharge Effects

S. Charles, J.-P. Mallet, H. Persat (2010)

Mathematical Modelling of Natural Phenomena

We propose a matrix population modelling approach in order to describe the dynamics of a grayling (Thymallus thymallus, L. 1758) population living in the Ain river (France). We built a Leslie like model, which integrates the climate changes in terms of temperature and discharge. First, we show how temperature and discharge can be related to life history traits like survival and reproduction. Second, we show how to use the population model to precisely examine the life cycle of grayling : estimated...

Positivity and contractivity in the dynamics of clusters’ splitting with derivative of fractional order

Emile Franc Doungmo Goufo, Stella Mugisha (2015)

Open Mathematics

Classical models of clusters’ fission have failed to fully explain strange phenomenons like the phenomenon of shattering (Ziff et al., 1987) and the sudden appearance of infinitely many particles in some systems with initial finite particles number. Furthermore, the bounded perturbation theorem presented in (Pazy, 1983) is not in general true in solution operators theory for models of fractional order γ (with 0 < γ ≤ 1). In this article, we introduce and study a model that can be understood as...

Pre-symptomatic Influenza Transmission, Surveillance, and School Closings: Implications for Novel Influenza A (H1N1)

G. F. Webb, Y-H. Hsieh, J. Wu, M. J. Blaser (2010)

Mathematical Modelling of Natural Phenomena

Early studies of the novel swine-origin 2009 influenza A (H1N1) epidemic indicate clinical attack rates in children much higher than in adults. Non-medical interventions such as school closings are constrained by their large socio-economic costs. Here we develop a mathematical model to ascertain the roles of pre-symptomatic influenza transmission as well as symptoms surveillance of children to assess the utility of school closures. Our model analysis...

Properties of a singular value decomposition based dynamical model of gene expression data

Krzysztof Simek (2003)

International Journal of Applied Mathematics and Computer Science

Recently, data on multiple gene expression at sequential time points were analyzed using the Singular Value Decomposition (SVD) as a means to capture dominant trends, called characteristic modes, followed by the fitting of a linear discrete-time dynamical system in which the expression values at a given time point are linear combinations of the values at a previous time point. We attempt to address several aspects of the method. To obtain the model, we formulate a nonlinear optimization problem...

Currently displaying 301 – 320 of 418