One of the most important problems in option pricing theory is the valuation and optimal exercise of derivatives with American-style exercise features. These types of derivatives are found in all major financial markets. Simulation is a promising alternative to traditional numerical methods and has many advantages as a framework for valuing American options. Recently, Longstaff and Schwartz presented a simple, yet powerful, least-squares Monte Carlo (LSM) algorithm to approximating the value of US options by simulation. This article provides computational complexity analysis of the LSM algorithm. Essentially, the technique of computational complexity analysis is to break down a computational algorithm into logical modules and analyze the effect on the algorithm of adding or deleting logical modules. Computational complexity analysis is important in algorithm design because of structural differences in computer and human logic. Algorithms that seem perfectly natural and logical from the human perspective may sometime be found to contain unnecessary complexity when analysed from the computer's perspective. The results showed that a new algorithm constructed by removing the least-squares module altogether from the LSM algorithm improves not only the computational speed, but also produces results that are more accurate than the LSM.
Design of a floating structure is supposed to be based on the extreme responses experienced by the components of the structure during its lifetime. The airgap response and potential deck impact of ocean structures under sea waves is of considerable interest. Non-linear diffraction models are usually called for a more consistent evaluation of the wave field under the deck and the wave run-up upon the columns, but even second-order analysis is not free of uncertainties. Therefore, air gap evaluation still relies heavily on experimental analysis. This paper presents some deep-tank results performed for the evaluation of the dynamic airgap of a large-volume semisubmersible platform. A series of model tests were carried out for the scale model of a horizontal moored semi in regular and extreme irregular wave conditions. Airgap response combined with run-up close to columns at total 11 locations on the deck was evaluated under oblique wave status. Motions and elevation data are analyzed by statistical treatment. Weibull-tail fitting procedure is realized to determine the extreme response levels.
In the Monte Carlo algorithm, the power iteration method is commonly used to obtain the Fission Neutron Bank of each cycle. This method uses the offspring produced by the neutrons of the previous cycle as the next cycle’s fission neutron bank. Thus, there is physical continuity between the adjacent cycle’s fission source distributions (FSD). This physical continuity of this process will lead to the mathematical correlation of fission source distributions. We extensively investigate the correlation of fission source distributions using mathematical approaches. We analyzed the correlations of the FSD with different geometric scales and the adjacent number of cycles. The results show that the correlations between two fission source distributions decline with the adjacent cycle number increases. The miniature models would take dozes of cycles for the correlations to decline to be negligible, while the standard reactor core model would use around 500 cycles to decline. These correlations should be carefully removed if a non-bias Monte Carlo calculation is carried out. In the BEAVRS core model, the correlations would result in around 80 percent underestimating the variance for the flux tally of assemblies. These methods can be easily implemented in the standard Monte Carlo codes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.