Generalized Stochastic Integration and Financial Modeling

Christos Floros, Konstantinos Gkillas and Christos Kountzakis
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Christos Floros: Department of Accounting and Finance, Hellenic Mediterranean University, Heraklion, Greece
Konstantinos Gkillas: ��Department of Management Science and Technology, University of Patras, Patras, Greece
Christos Kountzakis: ��Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Samos, Greece

Annals of Financial Economics (AFE), 2024, vol. 19, issue 03, 1-14

Abstract: In this paper, we establish a stochastic integral, relying on the order-complete vector lattices’ properties. This stochastic integral is alike to the Riemann integral on bounded real-valued functions. This integral’s properties provide stochastic integration of stochastic processes beyond integral, with respect to some Brownian motion. The Arrhenius equation, which is actually an essential equation in Physical Chemistry, does provide a capital transfer model between two assets in a specific portfolio. The Arrhenius equation is actually modified under this stochastic integral. The stochastic term of such a stochastic process is alike to the introduction of the “white noise†in stochastic integration, with respect to some Brownian motion.

Keywords: Stochastic integration; order-complete vector lattices; Arrhenius equation; capital transfer (search for similar items in EconPapers)
JEL-codes: C65 D53 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S2010495224500143

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