The authors report on the construction of a new algorithm for the weak approximation of stochastic differential equations. In this algorithm, an ODE-valued random variable whose average approximates the solution of the given stochastic differential equation is constructed by using the notion of free Lie algebras. It is proved that the classical Runge-Kutta method for ODEs is directly applicable to the ODE drawn from the random variable. In a numerical experiment, this is applied to the problem of pricing Asian options under the Heston stochastic volatility model. Compared with some other methods, this algorithm is significantly faster.
This paper demonstrates the application of a new higher-order weak approximation, called the Kusuoka approximation, with discrete random variables to non-commutative multi-factor models. Our experiments show that using the Heath-Jarrow-Morton model to price interestrate derivatives can be practically feasible if the Kusuoka approximation is used along with the tree-based branching algorithm.
The main theme of this research is numerical verification of applicability of a higher-order approximation to pricing barrier options, which is a both mathematically and practically important path-dependent type problem in mathematical finance. The authors successfully extend two types of algorithms called NV and NN. Both algorithms are based on a higher-order approximation scheme called Kusuoka approximation and have been shown to attain second-order approximation of stochastic differential equations as long as applied to European-type problems. In extending the algorithms, the authors apply a function representing the probability of hitting a boundary. In the numerical experiments, these two algorithms are compared with the Euler-Maruyama scheme which is one of the most popular first-order approximation schemes. As a result, it is demonstrated that the speed of calculation of these two algorithms could be much higher than that of the Euler-Maruyama scheme extended by the same way. It is concluded that one of the keys to improvement of the results is the construction of the function for calculation of the probability of hitting a boundary.
GaN-based high electron mobility transistors (HEMTs) are expected to have high performance in base station applications. Recently, it was reported that the combination of the Poisson-Schrodinger method and cellular automaton method is effective for predicting the mobility of channel two-dimensional electron gas (2DEG) of GaN HEMTs. In the operation condition of HEMT, the surface electron density of the channel is on the order of 1013 cm-2, and the effect of degeneracy cannot be ignored in calculating the mobility. Since the electron distribution function is always stably obtained by the cellular automaton method, the degeneracy effect can be considered stably. In this paper, through the comparison of different degeneracy evaluation methods, the anisotropy of the electron distribution function under the electric field acceleration is clarified to affect the HEMT mobility prediction significantly.
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.