Volume 14, Issue 4

We firstly show how to formulate the finance problem as an integration problem so that QMC methods can be applied to it. Consequently, we introduce QMC approaches for the integration problems pertaining to the Poisson processes, compound Poisson processes and jump-diffusion processes underlying the Kou model. As opposed to increment-by-increment approaches, our approaches change the ordering of the variates in the integration problems to pack more variance into the opening dimensions. We report numerical experiments indicating that the approaches introduced achieve lower standard errors than the increment-by-increment approaches.

This article will be started with a fundamental observation on consecutive non-negative integers. Based on the observation, we will demonstrate that the sequence of non-negative integers is regarded as a uniformly distributed sequence in the ring of the p -adic integers. As a result, the sequence provides us with a faster rate of convergence than the one obtained by simply applying law of the iterated logarithm.

Large eddy simulations involving dynamic subgrid-scale stress models reveal questions regarding the formulation of dynamic stress models. The dynamic Smagorinsky model, for example, yields large fluctuations and can easily become unstable. An analysis explains the reasons for these problems: it is shown that the dynamic Smagorinsky model involves an incorrect scale dependence which may produce significant errors leading to instabilities. These problems are addressed by analyzing the implications of the realizability constraint, this means the constraint that an acceptable turbulence closure model be based on the statistics of a velocity field that is physically achievable or realizable. The realizable dynamic stress models obtained have strong theoretical support: these models are the result of a well based systematic development of stress models. From a practical point of view, the realizable dynamic stress models obtained have the advantage that they do not support the development of instabilities due to possibly huge model errors. It is also shown that the consideration of nonlinear dynamic stress models further improves the accuracy of simulations.

We are concerned with the problem of estimating temporal values of the volatility in the situation that the observation of the price process is contaminated by high frequency noise due to micro structural causes of the system. For the case that there is no such noise, we have presented in the preceding article ([S. Ogawa and K. Wakayama, On a real-time scheme for the estimation of volatility , Monte Carlo Methods and Appl. 13 (2007), pp. 99–116.]) a scheme that is simple enough but might work effectively in a real-time manner. The aim of the present note is to introduce a new scheme by making suitable modifications to the old scheme so that the new one still maintains the nice property of being a real-time estimator.

The use of probability density function (PDF) methods for turbulent combustion simulations is very attractive because arbitrary finite-rate chemistry can be exactly taken into account. PDF methods are well developed for non-premixed turbulent combustion. However, many real flames involve a variety of mixing regimes (non-premixed, partially-premixed and premixed turbulent combustion), and the development of PDF methods for partially-premixed and premixed turbulent combustion turned out to be a very challenging task. The paper shows a promising way to overcome this problem by extending existing PDF methods such that a variety of mixing regimes can be covered. The latter is done by a generalization of the standard scalar mixing frequency model. The generalized scalar mixing frequency model accounts for several relevant processes in addition to velocity-scalar correlations that are represented by the standard model for the mixing of scalars. The suitability of the new mixing frequency model is shown by applications to several premixed turbulent Bunsen flames which cover various regimes ranging from flamelet to distributed combustion. Comparisons to existing concepts focused on the inclusion of reaction effects in mixing frequency models for non-reacting scalars reveal the advantages of the new mixing frequency model. It is worth noting that the same methodology can be used in corresponding filter density function (FDF) methods.