arXiv subjects

Mohammad Jelodari Mamaghani

Publications and source records attributed to Mohammad Jelodari Mamaghani.

3 recordsLinked to original sources

arXiv2024

Log-Ergodic Dynamics in Stochastic Monetary Velocity: Theoretical Insights and Economic Implications

We suggest employing log-ergodic processes to simulate the velocity of money in an ergodic manner. Our approach sheds light on economic behavior, policy implications, and financial dynamics by maintaining long-term stability. By bridging theory and practice, the partially ergodic model helps analysts and policymakers comprehend and forecast velocity of money. The empirical analysis, using historical U.S. GDP and money supply data, demonstrates the model's effectiveness in capturing the long-term stability of the velocity of money. Key findings indicate that the log-ergodic model offers superior predictive power compared to traditional models, making it a valuable tool for policymakers to control economic factors in vital situations.

q-fin.GN↗

arXiv2024

Some Applications of Log-Ergodic Processes: Ergodic Trading Model and Call Option Pricing Using the Irrational Rotation

Due to the increasing popularity of futures trading among financial market participants, the risk management of these instruments is crucial. In this paper, we introduce a model for estimating the ideal time for leaving a trading position on a stock. Also, using ergodic theorems, we investigate the European call option pricing problem using a stochastic irrational rotation on the unit circle. Utilizing the properties of log-ergodic processes, we use the time average of the stochastic process of risky assets instead of expectations in our calculations.

math.PR↗

arXiv2023

Log-ergodicity: A New Concept for Modeling Financial Markets

Although financial models violate ergodicity in general, observing the ergodic behavior in the markets is not rare. Policymakers and market participants control the market behavior in critical and emergency states, which leads to some degree of ergodicity as their actions are intentional. In this paper, we define a parametric operator that acts on the space of positive stochastic processes, transforming a class of positive stochastic processes into mean-ergodic processes. With this mechanism, we extract the data regarding the ergodic behavior hidden in the financial model, apply it to mathematical finance, and establish a novel method for pricing contingent claims. We provide some empirical examples and compare the results with existing ones to demonstrate the efficacy of this new approach.

math.PR↗