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We lay the theoretical and mathematical foundations of the square root of Brownian motion and we prove the existence of such a process. In doing so, we consider Brownian motion on quantized noncommutative Riemannian manifolds and show how a set of stochastic processes on sets of complex numbers can be devised. This class of stochastic processes are shown to yield at the outset a Chapman–Kolmogorov equation with a complex diffusion coefficient that can be straightforwardly reduced to the Schrödinger equation. The existence of these processes has been recently shown numerically. In this work we provide an analogous support for the existence of the Chapman–Kolmogorov–Schrödinger equation for them, performing a Monte Carlo study. It is numerically seen as a Wick rotation can turn the heat kernel into the Schrödinger one, mapping such kernels through the corresponding stochastic processes. In this way, we introduce a new kind of improper complex stochastic process. This permits a reformulation of quantum mechanics using purely geometrical concepts that are strongly linked to stochastic processes. Applications to economics are also entailed.
Marco Frasca; Alfonso Farina; Moawia Alghalith. Quantized noncommutative Riemann manifolds and stochastic processes: The theoretical foundations of the square root of Brownian motion. Physica A: Statistical Mechanics and its Applications 2021, 577, 126037 .
AMA StyleMarco Frasca, Alfonso Farina, Moawia Alghalith. Quantized noncommutative Riemann manifolds and stochastic processes: The theoretical foundations of the square root of Brownian motion. Physica A: Statistical Mechanics and its Applications. 2021; 577 ():126037.
Chicago/Turabian StyleMarco Frasca; Alfonso Farina; Moawia Alghalith. 2021. "Quantized noncommutative Riemann manifolds and stochastic processes: The theoretical foundations of the square root of Brownian motion." Physica A: Statistical Mechanics and its Applications 577, no. : 126037.
Summary We show that, in practice, the standard unit root tests, cointegration tests, and similar tests are unreliable. This conclusion is more generally applicable to other related regression-based tests. In particular, these tests attempt to solve a problem by creating another problem.
Moawia Alghalith. A note on the irrelevance of unit root tests and cointegration tests. Biometrical Letters 2020, 57, 85 -87.
AMA StyleMoawia Alghalith. A note on the irrelevance of unit root tests and cointegration tests. Biometrical Letters. 2020; 57 (1):85-87.
Chicago/Turabian StyleMoawia Alghalith. 2020. "A note on the irrelevance of unit root tests and cointegration tests." Biometrical Letters 57, no. 1: 85-87.
We propose novel nonparametric estimators for stochastic volatility and the volatility of volatility. In doing so, we relax the assumption of a constant volatility of volatility and therefore, we allow the volatility of volatility to vary over time. Our methods are exceedingly simple and far simpler than the existing ones. Using intraday prices for the Standard & Poor’s 500 equity index, the estimates revealed strong evidence that both volatility and the volatility of volatility are stochastic. We also proceeded in a Monte Carlo simulation analysis and found that the estimates were reasonably accurate. Such evidence implies that the stochastic volatility models proposed in the literature with constant volatility of volatility may fail to approximate the discrete-time short rate dynamics.
Moawia Alghalith; Christos Floros; Konstantinos Gkillas. Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility. Risks 2020, 8, 35 .
AMA StyleMoawia Alghalith, Christos Floros, Konstantinos Gkillas. Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility. Risks. 2020; 8 (2):35.
Chicago/Turabian StyleMoawia Alghalith; Christos Floros; Konstantinos Gkillas. 2020. "Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility." Risks 8, no. 2: 35.
We overcome a major obstacle in the literature. In doing, we introduce a simple, closed-form formula for pricing the American options. In particular, we significantly simplify Alghalith’s closed-form formula for pricing American options. In doing so, we introduce a formula that does not require the unknown expected consumption φ. This is a vast simplification, since the estimation of φ is challenging. That is, similar to a European option, we only need to know the interest rate and volatility. Furthermore, we derive an exact upper bound for the price.
Moawia Alghalith. Pricing the American options: A closed-form, simple formula. Physica A: Statistical Mechanics and its Applications 2019, 548, 123873 .
AMA StyleMoawia Alghalith. Pricing the American options: A closed-form, simple formula. Physica A: Statistical Mechanics and its Applications. 2019; 548 ():123873.
Chicago/Turabian StyleMoawia Alghalith. 2019. "Pricing the American options: A closed-form, simple formula." Physica A: Statistical Mechanics and its Applications 548, no. : 123873.
We overcome the limitations of the previous literature in the European options pricing. In doing so, we provide a closed-form formula that does not require any numerical/computational methods. The formula is as simple as the classical Black–Scholes pricing formula. In addition, we simultaneously include jumps and stochastic volatility. Our approach implies the introduction of a new class of stochastic processes that are based on Clifford algebras. The approach can be easily generalized to higher dimensional problems.
Moawia Alghalith. Pricing options under simultaneous stochastic volatility and jumps: A simple closed-form formula without numerical/computational methods. Physica A: Statistical Mechanics and its Applications 2019, 540, 123100 .
AMA StyleMoawia Alghalith. Pricing options under simultaneous stochastic volatility and jumps: A simple closed-form formula without numerical/computational methods. Physica A: Statistical Mechanics and its Applications. 2019; 540 ():123100.
Chicago/Turabian StyleMoawia Alghalith. 2019. "Pricing options under simultaneous stochastic volatility and jumps: A simple closed-form formula without numerical/computational methods." Physica A: Statistical Mechanics and its Applications 540, no. : 123100.
Summary We develop a simple method that completely eliminates the specification error and spurious relationships in regression. Furthermore, we introduce a stronger test of causality. We apply our method to oil prices.
Moawia Alghalith. A simple solution to the specification error. Biometrical Letters 2019, 56, 13 -16.
AMA StyleMoawia Alghalith. A simple solution to the specification error. Biometrical Letters. 2019; 56 (1):13-16.
Chicago/Turabian StyleMoawia Alghalith. 2019. "A simple solution to the specification error." Biometrical Letters 56, no. 1: 13-16.
Purpose This paper aims to quantify preferences without having to have any utility data. Design/methodology/approach We use duality theory, Taylor’s theorem and nonlinear regressions. Findings We presented pioneering quantitative methods in economics and business. These methods can be applied to numerous topics in empirical and theoretical economics and business. Moreover, this paper highlighted the interdisciplinary nature of economics. In doing so, it emphasized the interface between economics, marketing, management, statistics and mathematics. Furthermore, it circumvented a major obstacle in the literature: the curse of dimensionality. Originality/value The authors introduce a novel and convenient approach to utility modeling. In doing so, they present a general utility function in a simple form. Furthermore, they develop a method to measure preferences without any utility data. They also devise a method to measure the marginal utility. Then, they develop new methods of modeling and measuring the consumer utility. In so doing, they overcome a major obstacle: the curse of the dimensionality. In addition, they introduce new methods of modeling and measuring the consumer demand for the firm’s good.
Moawia Alghalith. New methods of modeling and estimating preferences. Studies in Economics and Finance 2019, 36, 83 -88.
AMA StyleMoawia Alghalith. New methods of modeling and estimating preferences. Studies in Economics and Finance. 2019; 36 (1):83-88.
Chicago/Turabian StyleMoawia Alghalith. 2019. "New methods of modeling and estimating preferences." Studies in Economics and Finance 36, no. 1: 83-88.
We significantly extend Alghalith (2017). In doing so, we show that the joint probability density can be estimated without knowing any of the marginal densities or the conditional density. Moreover, we provide a simpler, superior alternative to copulas.
Moawia Alghalith. A new parametric method of estimating the joint probability density: Revisited. Physica A: Statistical Mechanics and its Applications 2019, 527, 121455 .
AMA StyleMoawia Alghalith. A new parametric method of estimating the joint probability density: Revisited. Physica A: Statistical Mechanics and its Applications. 2019; 527 ():121455.
Chicago/Turabian StyleMoawia Alghalith. 2019. "A new parametric method of estimating the joint probability density: Revisited." Physica A: Statistical Mechanics and its Applications 527, no. : 121455.
We develop a simple, exact, explicit, and analytical solution to the American option partial differential equation PDE using the Black–Scholes pricing formula.
Moawia Alghalith. Pricing the American options using the Black–Scholes pricing formula. Physica A: Statistical Mechanics and its Applications 2018, 507, 443 -445.
AMA StyleMoawia Alghalith. Pricing the American options using the Black–Scholes pricing formula. Physica A: Statistical Mechanics and its Applications. 2018; 507 ():443-445.
Chicago/Turabian StyleMoawia Alghalith. 2018. "Pricing the American options using the Black–Scholes pricing formula." Physica A: Statistical Mechanics and its Applications 507, no. : 443-445.
Summary We introduce a method that eliminates the specification error and spurious relationships in regression. In addition, we introduce a test of strong causality. Furthermore, hypothesis testing (inference) becomes almost unneeded. Moreover, this method virtually resolves error problems such as heteroscedasticity, autocorrelation, non-stationarity and endogeneity.
Moawia Alghalith. The perfect regression and causality test: A solution to regression problems. Biometrical Letters 2018, 55, 45 -48.
AMA StyleMoawia Alghalith. The perfect regression and causality test: A solution to regression problems. Biometrical Letters. 2018; 55 (1):45-48.
Chicago/Turabian StyleMoawia Alghalith. 2018. "The perfect regression and causality test: A solution to regression problems." Biometrical Letters 55, no. 1: 45-48.
A new approach to jump diffusion is introduced, where the jump is treated as a vertical shift of the price (or volatility) function. This method is simpler than the previous methods and it is applied to the portfolio model with a stochastic volatility. Moreover, closed-form solutions for the optimal portfolio are obtained. The optimal closed-form solutions are derived when the value function is not smooth, without relying on the method of viscosity solutions.
Moawia Alghalith. A NOTE ON A NEW APPROACH TO BOTH PRICE AND VOLATILITY JUMPS: AN APPLICATION TO THE PORTFOLIO MODEL. The ANZIAM Journal 2016, 58, 182 -186.
AMA StyleMoawia Alghalith. A NOTE ON A NEW APPROACH TO BOTH PRICE AND VOLATILITY JUMPS: AN APPLICATION TO THE PORTFOLIO MODEL. The ANZIAM Journal. 2016; 58 (2):182-186.
Chicago/Turabian StyleMoawia Alghalith. 2016. "A NOTE ON A NEW APPROACH TO BOTH PRICE AND VOLATILITY JUMPS: AN APPLICATION TO THE PORTFOLIO MODEL." The ANZIAM Journal 58, no. 2: 182-186.
Highlights•Simple non-parametric methods that overcome key limitations of the existing literature on both the joint and marginal density estimation.•Does not assume any form of the marginal distribution or joint distribution a priori.•The method circumvents the bandwidth selection problems.•Compare our method to the kernel density method. AbstractWe introduce very simple non-parametric methods that overcome key limitations of the existing literature on both the joint and marginal density estimation. In doing so, we do not assume any form of the marginal distribution or joint distribution a priori. Furthermore, our method circumvents the bandwidth selection problems. We compare our method to the kernel density method.
Moawia Alghalith. Novel and simple non-parametric methods of estimating the joint and marginal densities. Physica A: Statistical Mechanics and its Applications 2016, 454, 94 -98.
AMA StyleMoawia Alghalith. Novel and simple non-parametric methods of estimating the joint and marginal densities. Physica A: Statistical Mechanics and its Applications. 2016; 454 ():94-98.
Chicago/Turabian StyleMoawia Alghalith. 2016. "Novel and simple non-parametric methods of estimating the joint and marginal densities." Physica A: Statistical Mechanics and its Applications 454, no. : 94-98.
Moawia Alghalith. Economic and Financial Informatics. Global Journal of Technology and Optimization 2016, 01, 1 -1.
AMA StyleMoawia Alghalith. Economic and Financial Informatics. Global Journal of Technology and Optimization. 2016; 01 (S1):1-1.
Chicago/Turabian StyleMoawia Alghalith. 2016. "Economic and Financial Informatics." Global Journal of Technology and Optimization 01, no. S1: 1-1.
Moawia Alghalith. Economic and Financial Informatics. Journal of Informatics and Data Mining 2016, 1, 1 .
AMA StyleMoawia Alghalith. Economic and Financial Informatics. Journal of Informatics and Data Mining. 2016; 1 (2):1.
Chicago/Turabian StyleMoawia Alghalith. 2016. "Economic and Financial Informatics." Journal of Informatics and Data Mining 1, no. 2: 1.
Moawia Alghalith. Taylor's series for non-differentiable functions. Mathematical Economics Letters 2014, 1 .
AMA StyleMoawia Alghalith. Taylor's series for non-differentiable functions. Mathematical Economics Letters. 2014; ():1.
Chicago/Turabian StyleMoawia Alghalith. 2014. "Taylor's series for non-differentiable functions." Mathematical Economics Letters , no. : 1.
Moawia Alghalith. Taylor's series for non-differentiable functions. Mathematical Economics Letters 2014, 1, 1 .
AMA StyleMoawia Alghalith. Taylor's series for non-differentiable functions. Mathematical Economics Letters. 2014; 1 (2-4):1.
Chicago/Turabian StyleMoawia Alghalith. 2014. "Taylor's series for non-differentiable functions." Mathematical Economics Letters 1, no. 2-4: 1.
This paper examines the interaction between consumption and the price/return of stocks. In so doing, we utilise an advanced theoretical and empirical framework. It is worth noting that previous literature used simple linear regressions without a rigorous theoretical basis. Consequently, we present a sophisticated non-linear dynamic model as the theoretical basis of our empirical results.
Moawia Alghalith; Tracy Polius. The Relationship between the Stock Market and Consumption. Economic Papers: A journal of applied economics and policy 2013, 32, 135 -138.
AMA StyleMoawia Alghalith, Tracy Polius. The Relationship between the Stock Market and Consumption. Economic Papers: A journal of applied economics and policy. 2013; 32 (1):135-138.
Chicago/Turabian StyleMoawia Alghalith; Tracy Polius. 2013. "The Relationship between the Stock Market and Consumption." Economic Papers: A journal of applied economics and policy 32, no. 1: 135-138.
We present a new method of estimating the volatility without data series for the volatility.
Moawia Alghalith. New methods of estimating volatility and returns: Revisited. Journal of Asset Management 2012, 13, 307 -309.
AMA StyleMoawia Alghalith. New methods of estimating volatility and returns: Revisited. Journal of Asset Management. 2012; 13 (5):307-309.
Chicago/Turabian StyleMoawia Alghalith. 2012. "New methods of estimating volatility and returns: Revisited." Journal of Asset Management 13, no. 5: 307-309.
We derive general explicit solutions to the investment model without reliance on the existing duality or variational methods.
Moawia Alghalith. A New Approach to Stochastic Optimization. Journal of Optimization Theory and Applications 2012, 155, 669 -672.
AMA StyleMoawia Alghalith. A New Approach to Stochastic Optimization. Journal of Optimization Theory and Applications. 2012; 155 (2):669-672.
Chicago/Turabian StyleMoawia Alghalith. 2012. "A New Approach to Stochastic Optimization." Journal of Optimization Theory and Applications 155, no. 2: 669-672.
Using the portfolio model, we introduce a general stochastic process that is not necessarily a diffusion/jump process and the random variable is not necessarily normally distributed
Moawia Alghalith. Generalized Stochastic Processes: The Portfolio Model. Journal of Mathematical Finance 2012, 02, 199 -201.
AMA StyleMoawia Alghalith. Generalized Stochastic Processes: The Portfolio Model. Journal of Mathematical Finance. 2012; 02 (02):199-201.
Chicago/Turabian StyleMoawia Alghalith. 2012. "Generalized Stochastic Processes: The Portfolio Model." Journal of Mathematical Finance 02, no. 02: 199-201.