Radka P. Koleva

This paper extends the optimal investment control framework by incorporating fractional Brownian motion to capture long-range dependence and memory effects in asset prices. Replacing the standard Brownian component with a fractional Brownian motion governed by the Hurst parameter H with $H\in (1/2,1)$, we employ the Wick–Itô calculus to derive the associated Hamilton–Jacobi–Bellman (HJB) equation. The resulting nonlinear PDE contains a time-dependent diffusion coefficient that reduces to the classical model when $H={\displaystyle \frac{1}{2}}$. We apply a linearized generalized Newton method to construct an iterative sequence for the value function and provide a numerical convergence analysis via the contraction mapping theorem. Using real GOOGL data, we obtain a model-implied mean optimal allocation of ${\overline{\pi }}^{*}=68.35\%$ for $H=0.62$, close to the classical $69.76\%$. A comprehensive sensitivity analysis identifies volatility $\sigma$ and jump intensity $\lambda$ as the dominant drivers of the optimal allocation, with absolute effects of $9.44\%$ and $6.47\%$, respectively, while the Hurst parameter H, the jump threshold $\tau$, and mean return $\alpha$ have smaller effects. The proposed framework provides a dynamic optimal investment ratio ${\pi }^{*}\left(t\right)$ that adjusts to market memory, offering a model-based strategy for portfolio management under both jump and long-memory risks. Empirical validation through backtesting is needed to establish its practical superiority.

The widespread application of plain S235JR steel across various industries often involves its exposure to degradative conditions, such as the organic acid concentrations typically found in various foodstuffs. This study investigates the corrosion behavior of S235JR steel immersed in several common beverages. The corrosion of steel S235JR was evaluated by gravimetric and electrochemical study. Statistical modeling via multiple linear regression and ANOVA was utilized to verify the experimental dataset. Based on the results, the highest early-stage corrosion occurs in coffee and tomato juice, though apple cider vinegar stands out for its steadily intensifying corrosive effect over the immersion period. Conversely, the presence of citric acid in lemon and orange juices appears to act as an inhibitor, leading to the lowest observed corrosion rates. The strong correlation between electrochemical parameters ($I_{corr}$ and $E_{ocp}$) and physical mass loss confirms that the chemical nature of each beverage significantly governs the corrosion kinetics of S235JR.