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Keywords = Feller’s criteria

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21 pages, 308 KiB  
Article
Ergodicity and Mixing Properties for SDEs with α-Stable Lévy Noises
by Siyan Xu and Huiyan Zhao
Axioms 2025, 14(2), 98; https://doi.org/10.3390/axioms14020098 - 28 Jan 2025
Viewed by 540
Abstract
In this paper, we consider a class of stochastic differential equations driven by multiplicative α-stable (0<α<2) Lévy noises. Firstly, we show that there exists a unique strong solution under a local one-sided Lipschitz condition and a [...] Read more.
In this paper, we consider a class of stochastic differential equations driven by multiplicative α-stable (0<α<2) Lévy noises. Firstly, we show that there exists a unique strong solution under a local one-sided Lipschitz condition and a general non-explosion condition. Next, the weak Feller and stationary properties are derived. Furthermore, a concrete sufficient condition for the coefficients is presented, which is different from the conditions for SDEs driven by Brownian motion or general squared-integrable martingales. Finally, some ergodic and mixing properties are obtained by using the Foster–Lyapunov criteria. Full article
12 pages, 536 KiB  
Article
A Divestment Model: Migration to Green Energy Investment Portfolio Concept
by Gaoganwe Sophie Moagi, Obonye Doctor and Edward Lungu
Mathematics 2024, 12(6), 915; https://doi.org/10.3390/math12060915 - 20 Mar 2024
Viewed by 1199
Abstract
In a targeted terminal wealth generated by bond and risky assets, where the proportion of a risky asset is gradually being phased down, we propose a divestment model in a risky asset compensated by growth in a bond (insurance). The model includes the [...] Read more.
In a targeted terminal wealth generated by bond and risky assets, where the proportion of a risky asset is gradually being phased down, we propose a divestment model in a risky asset compensated by growth in a bond (insurance). The model includes the phase-down rate of the risky asset, c(t), the variable proportion, π(t), in a risky asset and the interest rate, r, of the bond. To guide the growth of the total wealth in this study, we compared it to the Øksendal and Sulem (Backward Stochastic Differential Equations and Risk Measures (2019)) total wealth for which c(t)=0, and π(t) is a constant. We employed the Fokker–Planck equation to find the variable moment, π(t), and the associated variance. We proved the existence and uniqueness of the first moment by Feller’s criteria. We have found a pair (c*(t),r*) for each π(t), which guarantees a growing total wealth. We have addressed the question whether this pair can reasonably be achieved to ensure an acceptable phase-down rate at a financially achievable interest rate, r*. Full article
(This article belongs to the Special Issue Financial Mathematics and Applications)
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