Due to copyright restrictions, the access to the full text of this article is only available via subscription.In the present paper, the two-step difference scheme for the Cauchy problem for the stochastic hyperbolic equation is presented. The convergence estimate for the solution of the difference scheme is established. In applications, the convergence estimates for the solution of difference schemes for the numerical solution of four problems for hyperbolic equations are obtained. The theoretical statements for the solution of this difference scheme are supported by the results of the numerical experiment

Financial pricing and prediction of stock markets is a specific and relatively narrow field, which have been mainly explored by mathematicians, economists and financial engineers. Prediction with the purpose of making profits in a martingale domain is a hard task. Pairs trading, a market neutral arbitrage strategy, attempts to resolve the drawback of unpredictability and yield market independent returns using relative pricing idea. If two securities have similar characteristics, so should their prices. Deviation from the acceptable similarity range in prices is considered an anomaly, and whenever noticed, trading is executed assuming the anomaly will correct itself.This work proposes a fuzzy inference model for the market-neutral pairs trading strategy. Fuzzy logic lets mimicking human decision-making in a complex trading environment and taking advantage of arbitrage opportunities that the crisp models may miss to acquire for the trade decision-making. Spread between two co-integrated stocks and volatility of the spread is used as decision-making inputs. Spread is a measure of the distance between two stocks and volatility is an indicator of how soon the spread would disappear. We conclude that fuzzy engine contributes to the profitability and efficiency of pairs trading type of strategies.

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Due to copyright restrictions, the access to full text of this article is only available via subscriptionIn the present paper the two-step difference scheme for the telegraph equation is presented. The convergence estimate for the solution of the difference scheme is established. In applications, the convergence estimates for the solution of difference scheme for the numerical solution of two problems for hyperbolic equations are obtained. The theoretical statements for the solution of this difference scheme are supported by the results of the numerical experiment

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