Browsing Department of Mathematics and Statistics by Title
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Advances in periodic difference equations with open problems
(Springer, 2014)In this paper, we review some recent results on the dynamics of semidynamical systems generated by the iteration of a periodic sequence of continuous maps. In particular, we state several open problems focused on the ... 
Basin of Attraction through Invariant Curves and Dominant Functions
(Hindawi, 2015)We study a secondorder difference equation of the form 𝑧ₙ₊₁= 𝑧ₙ𝐹(𝑧ₙ₋₁) + ℎ, where both 𝐹(𝑧) and 𝑧𝐹(𝑧) are decreasing. We consider a set of invariant curves at ℎ = 1 and use it to characterize the behaviour of ... 
The Beverton–Holt model with periodic and conditional harvesting
(Taylor & Francis Online, 2009)In this theoretical study, we investigate the effect of different harvesting strategies on the discrete Beverton–Holt model in a deterministic environment. In particular, we make a comparison between the constant, periodic ... 
Can HighOrder Convergence of European Option Prices be Achieved with Common CRRType Binomial Trees?
(Springer, 2015)Considering European call options, we prove that CRRtype binomial trees systematically underprice the value of these options, when the spot price is not near the money. However, we show that, with a volatility premium to ... 
Coexistence and extinction in a competitive exclusion Leslie/Gower model with harvesting and stocking
(Taylor & Francis Online, 2009)The principle of competitive exclusion states that when the competition between species is sufficiently strong, only the dominant species survives. In this paper, we examine the strategies of using stocking and harvesting ... 
Control of cardiac alternans by mechanical and electrical feedback
(American Physical Society, 2014)A persistent alternation in the cardiac action potential duration has been linked to the onset of ventricular arrhythmia, which may lead to sudden cardiac death. A coupling between these cardiac alternans and the intracellular ... 
Convergence rate of regimeswitching trees
(Elseveir, 2016)Considering a general class of regimeswitching geometric random walks and a broad class of piecewise twice differentiable payoff functions, we show that convergence of option prices occurs at a speed of order 𝒪 (𝑛ᵝ), ... 
Convergence rate of the binomial tree scheme for continuously paying options
(Université du Québec à Montréal, 2012)Continuously Paying Options (CPOs) form a very natural class of derivatives for hedging risks coming from adverse movements of a continuously traded asset. We study the rate of convergence of CPOs evaluated under the ... 
The Discrete BevertonHolt Model with Periodic Harvesting in a Periodically Fluctuating Environment
(Springer, 2010)We investigate the effect of constant and periodic harvesting on the BevertonHolt model in a periodically fluctuating environment. We show that in a periodically fluctuating environment, periodic harvesting gives a better ... 
The dynamics of some discrete models with delay under the eﬀect of constant yield harvesting
(Elsevier, 2013)In this paper, we study the dynamics of population models of the form xn+1 = xnf(xn−1) under the eﬀect of constant yield harvesting. Results concerning stability, boundedness, persistence and oscillations of solutions are ... 
A European option general firstorder error formula
(Cambridge, 2013)We study the value of European security derivatives in the BlackScholes model, when the underlying asset 𝛏 is approximated by random walks 𝛏(𝑛). We obtain an explicit error formula, up to a term of order 𝒪(𝑛⁻³/² ), ... 
Exercisability Randomization of the American Option
(Taylor & Frances Online, 2008)The valuation of American options is an optimal stopping time problem which typically leads to a free boundary problem. We introduce here the randomization of the exercisability of the option. This method considerably ... 
Existence and stability of periodic orbits of periodic difference equations with delays
(World Scientific Publishing, 2008)In this paper, we investigate the existence and stability of periodic orbits of the pperiodic difference equation with delays xₙ = f(n  1, xₙ₋ₖ). We show that the periodic orbits of this equation depend on the periodic ... 
An Extension of Sharkovsy’s Theorem to Periodic Difference Equations
(Elsevier, 2006)We present an extension of Sharkovsky’s Theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a pperiodic difference equation having an rperiodic geometric ... 
The eﬀect of maps permutation on the global attractor of a periodic BevertonHolt model
(Elsevier, 20200401)Consider a pperiodic diﬀerence equation xn+1 = fn(xn) with a global attractor. How does a permutation [fσ(p−1), . . . , fσ(1), fσ(0)] of the maps aﬀect the global attractor? In this paper, we limit this general question ... 
Folding and unfolding in periodic difference equations
(Elseiver, 2014)Given a pperiodic difference equation xn+1 = fn mod p(xn), where each fj is a continuous interval map, j = 0, 1, . . . , p − 1, we discuss the notion of folding and unfolding related to this type of nonautonomous equations. ... 
A Global Attractor in Some Discrete Contest Competition Models with Delay under the Effect of Periodic Stocking
(Hindawi, 2013)We consider discrete models of the form 𝒳ₙ₊₁= 𝒳ₙ𝒇(𝒳ₙ₋₁) + 𝒉ₙ , where 𝒉ₙ is a nonnegative 𝒑periodic sequence representing stocking in the population, and investigate their dynamics. Under certain conditions on the ... 
Harvesting and stocking in discretetime contest competition models with open problems and conjectures
(Palestine Polytechnic University, 2016)In this survey, we present a class of first and secondorder difference equations representing general form of discrete models arising from singlespecies with contest competition. Then, we consider various harvesting/stocking ... 
The impact of constant effort harvesting on the dynamics of a discretetime contest competition model
(Wiley, 2017)In this paper, we study a general discrete–time model representing the dynamics of a contest competition species with constant effort exploitation. In particular, we consider the difference equation xn+1 = xnf(xn−k) − hxn ... 
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, ...