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Pablo Amster

Publications and source records attributed to Pablo Amster.

25 records · Page 2Linked to original sources
arXiv2018

On a pricing problem for a multi-asset option with general transaction costs

We consider a Black-Scholes type equation arising on a pricing model for a multi-asset option with general transaction costs. The pioneering work of Leland is thus extended in two different ways: on the one hand, the problem is multi-dimensional since it involves different underlying assets; on the other hand, the transaction costs are not assumed to be constant (i.e. a fixed proportion of the traded quantity). In this work, we generalize Leland's condition and prove the existence of a viscosity solution for the corresponding fully nonlinear initial value problem using Perron method. Moreover, we develop a numerical ADI scheme to find an approximated solution. We apply this method on a specific multi-asset derivative and we obtain the option price under different pricing scenarios.

q-fin.CP↗
arXiv2018

On exact multiplicity for a second order equation with radiation boundary conditions

A second order ordinary differential equation with a superlinear term $g(x,u)$ under radiation boundary conditions is studied. Using a shooting argument, all the results obtained in a previous work for a Painlevé II equation are extended. It is proved that the uniqueness or multiplicity of solutions depend on the interaction between the mapping $\frac {\partial g}{\partial u}(\cdot,0)$ and the first eigenvalue of the associated linear operator. Furthermore, two open problems regarding, on the one hand, the existence of sign-changing solutions and, on the other hand, exact multiplicity are solved.

math.CA↗
arXiv2018

Multiple solutions for periodic perturbations of a delayed autonomous system near an equilibrium

Small non-autonomous perturbations around an equilibrium of a nonlinear delayed system are studied. Under appropriate assumptions, it is shown that the number of $T$-periodic solutions lying inside a bounded domain $Ω\subset \R^N$ is, generically, at least $|χ\pm 1|+1$, where $χ$ denotes the Euler characteristic of $Ω$. Moreover, some connections between the associated fixed point operator and the Poincaré operator are explored.

math.CA↗
arXiv2016

Systems of Delay Differential Equations: Analysis of a model with feedback

Self-regulatory models are common in nature, as described e.g. in (\cite{mur}), (\cite{ha}) and (\cite{Gb}).\\ Let us consider a system made up of a number of glands as a motivation. Each gland secretes a hormone that allows secretion in the {next} gland, which successively generates another hormone to stimulate the next one and so on. In the end, a final hormone is released which, by increasing its concentration, will inhibit the secretion of previous hormones that allowed the production process. This generates the decay of this hormone to a minimum threshold that re-activates the cycle again.\\ This behavior can be seen in other biochemical processes, such as enzymatic or bacterial models.\\ Topological degree is a useful tool to find stable equilibria in a wide variety of models with constant parameters and, furthermore, allows to deduce the existence of periodic solutions when the constant parameters are replaced by periodic functions.

math.DS↗
arXiv2013

On existence of periodic solutions for Kepler type problems

We prove existence and multiplicity of periodic motions for the forced 2-body problem under conditions of topological character. In the different cases, the lower bounds obtained for the number of solutions are related to the winding number of a curve in the plane, the homology of a space in $\R^3$, the knot type of a curve and the link type of a set of curves. Also, the results are applied to the restricted $n$-body problem.

math.CA↗