On the system of two nonlinear difference equations x

We study the oscillatory behavior, the periodicity and the asymptotic behavior of the positive solutions of the system of two nonlinear difference equations xn+1=A+xn−1/yn and yn+1=A+yn−1/xn, where A is a positive constant, and n=0,1,…

Hedging and non-hedging trading strategies on commodities using the d-Backtest PS method. Optimized trading system hedging

Modern trading systems are mechanic, run automatically on computers inside trading platforms and decide their position against the market through optimized parameters and algorithmic strategies. These systems now, in most cases, comprise high frequency traders, especially in the Forex market.In this research, a piece of software of an automatic high frequency trading system was developed, based on the technical indicator PIVOT (price level breakthrough). The system made transactions on hourly closing prices with weekly parameters optimization period, using the d-Backtest PS method.Through the search and checking of the results, two findings for optimization of trading strategy were found. These findings with the order they were examined and are presented in this paper are as follows: (1) the simultaneous use of “long and short” positions, with different parameters in a hedging account, acts as a hedging strategy, minimizing losses, in relation to a “long or short” in a non-hedging account for the same time period and (2) there is weak correlation of past backtesting periods between the same systems, if they are configured for “long and short” trades, or for just “long” or for just “short”

On the Recursive Sequence xn+1=A+(xn−1p/xnq)

In this paper we study the boundedness, the persistence, the attractivity and the stability of the positive solutions of the nonlinear difference equation xn+1=α+(xn−1p/xnq), n=0,1,…, where α,p,q∈(0,∞) and x−1,x0∈(0,∞). Moreover we investigate the existence of a prime two periodic solution of the above equation and we find solutions which converge to this periodic solution

On a k-Order System of Lyness-Type Difference Equations

We consider the following system of Lyness-type difference equations: x1(n+1)=(akxk(n)+bk)/xk−1(n−1), x2(n+1)=(a1x1(n)+b1)/xk(n−1), xi(n+1)=(ai−1xi−1(n)+bi−1)/xi−2(n−1), i=3,4,…,k, where ai, bi, i=1,2,…,k, are positive constants, k≥3 is an integer, and the initial values are positive real numbers. We study the existence of invariants, the boundedness, the persistence, and the periodicity of the positive solutions of this system

On the stability of some systems of exponential difference equations

In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations

Boundedness, Attractivity, and Stability of a Rational Difference Equation with Two Periodic Coefficients

We study the boundedness, the attractivity, and the stability of the positive solutions of the rational difference equation xn+1=(pnxn−2+xn−3)/(qn+xn−3), n=0,1,…, where pn,qn, n=0,1,… are positive sequences of period 2

On the stability of some systems of exponential difference equations

In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations