Browsing Department of Mathematics and Statistics by Title
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Joshi’s Split Tree for Option Pricing
(MDPI, 2020)In a thorough study of binomial trees, Joshi introduced the split tree as a twophase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American ... 
A Market Efficiency Comparison of Islamic and NonIslamic Stock Indices
(Taylor & Francis Online, 2015)This article examines the martingale difference hypothesis (MDH) and the random walk hypothesis (RWH) for nine conventional and nine Islamic stock indices: AsiaPacific, Canadian, Developed Country, Emerging, European, ... 
Market Efficiency of Floating Exchange Rate Systems: Some Evidence from PacificAsian Countries
(Elsevier, 2011)This paper examines the random walk hypothesis (RWH) and the martingale difference hypothesis (MDH) for the Australian dollar and five Asian emerging currencies relative to three benchmark currencies. We use Wright’s (2000) ... 
Martingale problem for superprocesses with nonclassical branching functional
(Elsevier, 2006)The martingale problem for superprocesses with parameters (𝛏, Ф, 𝑘) is studied where 𝑘(𝒹𝑠) may not be absolutely continuous with respect to the Lebesgue measure. This requires a generalization of the concept of ... 
Mechanical perturbation control of cardiac alternans
(American Physical Society, 2018)Cardiac alternans is a disturbance in heart rhythm that is linked to the onset of lethal cardiac arrhythmias. Mechanical perturbation control has been recently used to suppress alternans in cardiac tissue of relevant size. ... 
Modeling and simulation of hypothermia effects on cardiac electrical dynamics
(Public Library of Science, 2019)Previous experimental evidence has shown the effect of temperature on the action potential duration (APD). It has also been demonstrated that regional cooling of the heart can prolong the APD and promote the termination ... 
A new characterization of periodic oscillations in periodic difference equations
(Elsevier, 201111)In this paper, we characterize periodic solutions of pperiodic diﬀerence equations. We classify the periods into multiples of p and nonmultiples of p. We show that the elements of the set of multiples of p follow the ... 
On phiDedekind rings and phiKrull rings
(University of Houston, 2005)The purpose of this paper is to introduce two new classes of rings that are closely related to the classes of Dedekind domains and Krull domains. Let H = {R  R is a commutative ring with 1 and Nil(R) is a divided prime ... 
On phiMori rings
(University of Houston, 2006)A commutative ring R is said to be a phiring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map phi from the total quotient ring T(R) to R localized ... 
On the dot product graph of a commutative ring II
(International Electronic Journal of Algebra, 2020)In 2015, the secondnamed author introduced the dot product graph associated to a commutative ring A. Let A be a commutative ring with nonzero identity, 1 ≤ n < ∞ be an integer, and R = A × A × · · · × A (n times). We ... 
On the periodic logistic equation
(Elsevier, 2006)We show that the 𝒑periodic logistic equation 𝒳ₙ₊₁ = μₙ mod 𝒑𝒳ₙ(1  𝒳ₙ) has cycles (periodic solutions) of minimal periods 1; 𝒑; 2𝒑; 3𝒑; …. Then we extend Singer’s theorem to periodic difference equations, and use ... 
On weakly 2absorbing ideals of commutative rings
(University of Houston, 2013)Let R be a commutative ring with identity 1 not equal to 0. In this paper, we introduce the concept of a weakly 2absorbing ideal. A proper ideal I of R is called a weakly 2absorbing ideal of R if whenever abc is not equal ... 
Option convergence rate with geometric random walks approximations
(Taylor & Frances Online, 2016)We describe a broad setting under which, for European options, if the underlying asset form a geometric random walk then, the error with respect to the Black–Scholes model converges to zero at a speed of 1/𝑛 for continuous ... 
Path Independence of Exotic Options and Convergence of Binomial Approximations
(Infopro Digital Risk (IP), 2019)The analysis of the convergence of tree methods for pricing barrier and lookback options has been the subject of numerous publications aiming at describing, quantifying, and improving the slow and oscillatory convergence ... 
Periodic Orbits in Periodic Discrete Dynamics
(Elsevier, 2008)We study the combinatorial structure of periodic orbits of nonautonomous difference equations 𝒳ₙ₊₁ = 𝒇ₙ(𝒳ₙ) in a periodically fluctuating environment. We define the Ӷset to be the set of minimal periods that are not ... 
Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory
(De Gruyter, 2020)For a partially ordered set(A, ≤), letGA be the simple, undirected graph with vertex set A such that two vertices a ≠ ∈ b A are adjacent if either a ≤ b or b a ≤ . We call GA the partial order graph or comparability graph ... 
A robust method to retrieve option implied risk neutral densities for defaultable assets
(Inderscience Publishers, 2016)Risk neutral densities recovered from option prices can be used to infer market participants' expectations of future stock returns and are a vital tool for pricing illiquid exotic options. Although there is a broad literature ... 
The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology
(Taylor & Francis, 2013)One of the central problems in botanical epidemiology is whether disease spreads within crops in a regular pattern or follows a random process. In this paper, we consider a row of n plants in which m are infected. We then ... 
Some finiteness conditions on the set of overrings of a phiring
(University of Houston, 2008)Let H = {R  R is a commutative ring and Nil(R) is a divided prime ideal of R}. For a ring R in H with total quotient ring T(R), Let phi be the natural ring homomorphism from T(R) into R_Nil(R). An integral domain R is ...