Numerical solution of Black-Scholes option pricing with variable yield discrete dividend payment

Rafael Company; Lucas Jódar; Enrique Ponsoda

Displaying similar documents to “Numerical solution of Black-Scholes option pricing with variable yield discrete dividend payment”

The joint essential numerical range of operators: convexity and related results

Chi-Kwong Li, Yiu-Tung Poon (2009)

Studia Mathematica

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Let W(A) and $W_{e} (A)$ be the joint numerical range and the joint essential numerical range of an m-tuple of self-adjoint operators A = (A₁, ..., Aₘ) acting on an infinite-dimensional Hilbert space. It is shown that $W_{e} (A)$ is always convex and admits many equivalent formulations. In particular, for any fixed i ∈ 1, ..., m, $W_{e} (A)$ can be obtained as the intersection of all sets of the form $c l (W (A ₁, . . ., A_{i + 1}, A_{i} + F, A_{i + 1}, . . ., A ₘ))$ , where F = F* has finite rank. Moreover, the closure cl(W(A)) of W(A) is always star-shaped with the elements in...

The covariety of perfect numerical semigroups with fixed Frobenius number

María Ángeles Moreno-Frías, José Carlos Rosales (2024)

Czechoslovak Mathematical Journal

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Let $S$ be a numerical semigroup. We say that $h \in ℕ ∖ S$ is an isolated gap of $S$ if ${h - 1, h + 1} \subseteq S .$ A numerical semigroup without isolated gaps is called a perfect numerical semigroup. Denote by $m (S)$ the multiplicity of a numerical semigroup $S$ . A covariety is a nonempty family $𝒞$ of numerical semigroups that fulfills the following conditions: there exists the minimum of $𝒞,$ the intersection of two elements of $𝒞$ is again an element of $𝒞$ , and $S ∖ {m (S)} \in 𝒞$ for all $S \in 𝒞$ such that $S \neq min (𝒞) .$ We prove that the set $𝒫 (F) = {S : S$ is a perfect numerical semigroup...

The new iteration methods for solving absolute value equations

Rashid Ali, Kejia Pan (2023)

Applications of Mathematics

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Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations $A x - | x | = b$ , where $A \in ℝ^{n \times n}$ is an $M$ -matrix or strictly diagonally dominant matrix, $b \in ℝ^{n}$ and $x \in ℝ^{n}$ is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness...

Product of operators and numerical range preserving maps

Chi-Kwong Li, Nung-Sing Sze (2006)

Studia Mathematica

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Let V be the C*-algebra B(H) of bounded linear operators acting on the Hilbert space H, or the Jordan algebra S(H) of self-adjoint operators in B(H). For a fixed sequence (i₁, ..., iₘ) with i₁, ..., iₘ ∈ 1, ..., k, define a product of $A ₁, . . ., A_{k} \in V$ by $A ₁ * \dots * A_{k} = A_{i ₁} \dots A_{i ₘ}$ . This includes the usual product $A ₁ * \dots * A_{k} = A ₁ \dots A_{k}$ and the Jordan triple product A*B = ABA as special cases. Denote the numerical range of A ∈ V by W(A) = (Ax,x): x ∈ H, (x,x) = 1. If there is a unitary operator U and a scalar μ satisfying $μ^{m} = 1$ such that ϕ: V → V has...

Adding or removing an element from a pseudo-symmetric numerical semigroup

J. C. Rosales (2006)

Bollettino dell'Unione Matematica Italiana

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If $S$ is a pseudo-symmetric numerical semigroup, $g$ is its Frobenius number and $S$ is a minimal generator of $S$ , then $S\cup\{g\}$ , $S\setminus\{g\}$ S and $S\cup\{\frac{1}{2}g,g\}$ are also numerical semigroups. In this paper we study these constructions.

Nearstandardness on a finite set

Lyantse V.

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AbstractLet T be a finite set for which card T is a natural nonstandard number. The linear space $ℂ^{T}$ of complex-valued functions on T is nonstandard. For the analysis on $ℂ^{T}$ we need a concept of nearstandardness in this space. A version how to introduce such a concept is proposed. Some elementary examples are given. CONTENTSIntroduction.................................................................................................................50. Preliminary notes....................................................................................................7 0.1....

Computational results relating to problems concerning $σ (n)$

W. E. Mientka, R. L. Vogt (1970)

Matematički Vesnik

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When $C_{p} (X)$ is domain representable

William Fleissner, Lynne Yengulalp (2013)

Fundamenta Mathematicae

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Let M be a metrizable group. Let G be a dense subgroup of $M^{X}$ . We prove that if G is domain representable, then $G = M^{X}$ . The following corollaries answer open questions. If X is completely regular and $C_{p} (X)$ is domain representable, then X is discrete. If X is zero-dimensional, T₂, and $C_{p} (X,)$ is subcompact, then X is discrete.

Numerical approximation of the non-linear fourth-order boundary-value problem

Svobodová, Ivona

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We consider functionals of a potential energy $ℙ_{ψ} (u)$ corresponding to $𝑎𝑛 𝑎𝑥𝑖𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 - 𝑣𝑎𝑙𝑢𝑒 𝑝𝑟𝑜𝑏𝑙𝑒𝑚$ . We are dealing with $𝑎 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎 𝑡ℎ𝑖𝑛 𝑎𝑛𝑛𝑢𝑙𝑎𝑟 𝑝𝑙𝑎𝑡𝑒$ with $𝑁𝑒𝑢𝑚𝑎𝑛𝑛 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠$ . Various types of the subsoil of the plate are described by various types of the $𝑛𝑜𝑛𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑏𝑙𝑒$ nonlinear term $ψ (u)$ . The aim of the paper is to find a suitable computational algorithm.

Optimization problem under two-sided (max, +)/(min, +) inequality constraints

Karel Zimmermann (2020)

Applications of Mathematics

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$(max, +)$ -linear functions are functions which can be expressed as the maximum of a finite number of linear functions of one variable having the form $f (x_{1}, \dots, x_{h}) = {max}_{j} (a_{j} + x_{j})$ , where $a_{j}$ , $j = 1, \dots, h$ , are real numbers. Similarly $(min, +)$ -linear functions are defined. We will consider optimization problems in which the set of feasible solutions is the solution set of a finite inequality system, where the inequalities have $(max, +)$ -linear functions of variables $x$ on one side and $(min, +)$ -linear functions of variables $y$ on the other side....

Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices

David Cimasoni (2012)

Journal of the European Mathematical Society

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Let $\sum$ be a flat surface of genus $g$ with cone type singularities. Given a bipartite graph $Γ$ isoradially embedded in $\sum$ , we define discrete analogs of the $2^{2 g}$ Dirac operators on $\sum$ . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair $Γ \subset \sum$ for these discrete Dirac operators to be Kasteleyn matrices of the graph $Γ$ . As a consequence, if these conditions are met, the partition function...

Modeling of the resonance of an acoustic wave in a torus

Jérôme Adou, Adama Coulibaly, Narcisse Dakouri (2013)

Annales mathématiques Blaise Pascal

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A pneumatic tyre in rotating motion with a constant angular velocity $Ω$ is assimilated to a torus whose generating circle has a radius $R$ . The contact of the tyre with the ground is schematized as an ellipse with semi-major axis $a$ . When $(Ω R / C_{0}) ≪ 1$ and $(a / R) ≪ 1$ (where $C_{0}$ is the velocity of the sound), we show that at the rapid time scale $R / C_{0}$ , the air motion within a torus periodically excited on its surface generates an acoustic wave $h$ . A study of this acoustic wave is conducted and shows that the mode associated...

Numerical radius inequalities for Hilbert $C^{*}$ -modules

Sadaf Fakri Moghaddam, Alireza Kamel Mirmostafaee (2022)

Mathematica Bohemica

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We present a new method for studying the numerical radius of bounded operators on Hilbert $C^{*}$ -modules. Our method enables us to obtain some new results and generalize some known theorems for bounded operators on Hilbert spaces to bounded adjointable operators on Hilbert $C^{*}$ -module spaces.

Numerical stability of the intrinsic equations for beams in time domain

Klesa, Jan

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Intrinsic equations represent promising approach for the description of rotor blade dynamics. They are the system of non-linear partial differential equations. Stability of numeric solution by the finite difference method is described. The stability is studied for various numerical schemes with different methods for the computation of spatial derivatives from time level $n + 0.5$ (i.e., mean values of old and new time step) to $n + 1$ (i.e., only from new time step). Stable solution was obtained only...

Soft local times and decoupling of random interlacements

Serguei Popov, Augusto Teixeira (2015)

Journal of the European Mathematical Society

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In this paper we establish a decoupling feature of the random interlacement process $ℐ^{u} \subset ℤ^{d}$ at level $u$ , $d \geq 3$ . Roughly speaking, we show that observations of $ℐ^{u}$ restricted to two disjoint subsets $A_{1}$ and $A_{2}$ of $ℤ^{d}$ are approximately independent, once we add a sprinkling to the process $ℐ^{u}$ by slightly increasing the parameter $u$ . Our results differ from previous ones in that we allow the mutual distance between the sets $A_{1}$ and $A_{2}$ to be much smaller than their diameters. We then provide an important application...