A Mixed PDE/Monte Carlo approach as an efficient way to price under high-dimensional systems

We propose to price derivatives modelled by multi-dimensional systems of stochastic di�fferential\ud equations using a mixed PDE/Monte Carlo approach. We derive a stochastic PDE where some of the coeffi�cients are conditional on stochastic ancillary factors. The stochastic\ud PDE is solved with either analytical or �finite diff�erence methods, where we simulate all the ancillary processes using Monte Carlo. The multilevel technique has also been introduced to further reduce the variance. The combined method showed over 80% cost reduction for the same accuracy, in pricing a barrier option in an FX market with stochastic interest rate and volatility (which is usually expensive to work with) , when compared to the pure Monte\ud Carlo simulation

Removal Efficiency and Mechanism of Sulfamethoxazole in Aqueous Solution by Bioflocculant MFX

Although the treatment technology of sulfamethoxazole has been investigated widely, there are various issues such as the high cost, inefficiency, and secondary pollution which restricted its application. Bioflocculant, as a novel method, is proposed to improve the removal efficiency of PPCPs, which has an advantage over other methods. Bioflocculant MFX, composed by high polymer polysaccharide and protein, is the metabolism product generated and secreted by Klebsiella sp. In this paper, MFX is added to 1 mg/L sulfanilamide aqueous solution substrate, and the removal ratio is evaluated. According to literatures review, for MFX absorption of sulfanilamide, flocculant dosage, coagulant-aid dosage, pH, reaction time, and temperature are considered as influence parameters. The result shows that the optimum condition is 5 mg/L bioflocculant MFX, 0.5 mg/L coagulant aid, initial pH 5, and 1 h reaction time, and the removal efficiency could reach 67.82%. In this condition, MFX could remove 53.27% sulfamethoxazole in domestic wastewater, and the process obeys Freundlich equation. R2 value equals 0.9641. It is inferred that hydrophobic partitioning is an important factor in determining the adsorption capacity of MFX for sulfamethoxazole solutes in water; meanwhile, some chemical reaction probably occurs