New Algorithm for Stochastic Problems with Random Fields of Non-finite Variances | Chapter 01 | Current Research in Science and Technology Vol. 3
A new algorithm is developed to solve
stochastic problems with random fields of non-finite variances. Developing this
algorithm motives from an attempt of representing random fields following the
Lévy distribution. The first step of current algorithm is deriving moving least
square reproducing kernel (MLSRK) approximations of random fields. These MLSRK
approximations are derived over local support domains in the probability space.
Thus, equating such approximations is still possible, even if the variance of
random fields to be studied is infinite. The stochastic problem is next solved
with respect to these MLSRK approximations. Testing the succeeding algorithm
finds that it doesn't require many samples and any empirical coefficient to
represent accurately random fields following such as Lévy, Cauchy, and
multivariate Cauchy distributions. It also provides accurate computation of
means and variances of the option price with the stochastic volatility
following two empirical Pareto- Lévy and non-stable Lévy distributions. Except
for MLSRK approximations of the option price and stochastic volatility, such
computation is tested with a deterministic meshless collocation formulation of
the Black-Scholes equation.
Author(s) Details
Guang-Yih Sheu
Department of Accounting and
Information Systems, Chang-Jung Christian University, P.O.Box 701, Tainan,
Taiwan.
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