arXiv subjects

P. Amster

Publications and source records attributed to P. Amster.

3 recordsLinked to original sources

arXiv2025

A discrete one-species chemostat model with delayed response in the growth and non-constant supply

A non-autonomous discrete delayed system for a one-species chemostat based on an Ellermeyer model for the continuous case is studied. Conditions for the persistence or the extinction of the solutions are obtained respectively in terms of the lower and upper Bohl exponents for a scalar linear equation associated to the problem. Furthermore, the condition for persistence also implies the attractiveness, that is, the existence of a bounded solution that attracts all the others. As a special case, when the nutrient supply is $\omega$-periodic, the picture is complete: the condition for persistence implies the existence of an attractive non-trivial $\omega$-periodic solution, while non-persistence implies extinction.

math.DS↗

arXiv2018

Adapting the CVA model to Leland's framework

We consider the framework proposed by Burgard and Kjaer (2011) that derives the PDE which governs the price of an option including bilateral counterparty risk and funding. We extend this work by relaxing the assumption of absence of transaction costs in the hedging portfolio by proposing a cost proportional to the amount of assets traded and the traded price. After deriving the nonlinear PDE, we prove the existence of a solution for the corresponding initial-boundary value problem. Moreover, we develop a numerical scheme that allows to find the solution of the PDE by setting different values for each parameter of the model. To understand the impact of each variable within the model, we analyze the Greeks of the option and the sensitivity of the price to changes in all the risk factors.

q-fin.MF↗

arXiv2011

Stability of Hahnfeldt Angiogenesis Models with Time Lags

Mathematical models of angiogenesis, pioneered by P. Hahnfeldt, are under study. To enrich the dynamics of three models, we introduced biologically motivated time-varying delays. All models under study belong to a special class of nonlinear nonautonomous systems with delays. Explicit conditions for the existence of positive global solutions and the equilibria solutions were obtained. Based on a notion of an M-matrix, new results are presented for the global stability of the system and were used to prove local stability of one model. For a local stability of a second model, the recent result for a Lienard-type second-order differential equation with delays was used. It was shown that models with delays produce a complex and nontrivial dynamics. Some open problems are presented for further studies.

math.DS↗