Marginalization for rare event simulation in switching diffusions

In this paper we use splitting technique to estimate the probability of hitting a rare but critical set by the continuous component of a switching diffusion. Instead of following classical approach we use Wonham filter to achieve multiple goals including reduction of asymptotic variance and exemption from sampling the discrete components

The optimal hedging in a semi-Markov modulated market

This paper includes an original self contained proof of well-posedness of an initial-boundary value problem involving a non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. We call this market model a semi-Markov modulated market. Although a wellposedness result of that problem is available in the literature, but this recent paper has a different proof. Here the existence of solution is established without invoking mild solution technique. We study the well-posedness of the initial-boundary value problem via a Volterra integral equation of second kind. The method of conditioning on stopping times was used only for showing uniqueness. Furthermore, in the present study we find an integral representation of the PDE problem which enables us to find a robust numerical scheme to compute derivative of the solution. This study paves for addressing many other interesting problems involving this new set of PDEs. Some derivations of external cash flow corresponding to an optimal strategy are presented. These quantities are extremely important when dealing with an incomplete market. Apart from these, the risk measures for discrete trading are formulated which may be of interest to the practitioners.Comment: 23 pages, 4 figure

Semi-implicit Integration and Data-Driven Model Order Reduction in Structural Dynamics with Hysteresis

Structural damping is known to be approximately rate-independent in many cases. Popular models for rate-independent dissipation are hysteresis models; and a highly popular hysteresis model is the Bouc-Wen model. If such hysteretic dissipation is incorporated in a refined finite element model, then the mathematical model includes the usual structural dynamics equations along with nonlinear nonsmooth ordinary differential equations for a large number of internal hysteretic states at Gauss points, to be used within the virtual work calculation for dissipation. For such systems, numerical integration becomes difficult due to both the distributed non-analytic nonlinearity of hysteresis as well as the very high natural frequencies in the finite element model. Here we offer two contributions. First, we present a simple semi-implicit integration approach where the structural part is handled implicitly based on the work of Pich\'e, and where the hysteretic part is handled explicitly. A cantilever beam example is solved in detail using high mesh refinement. Convergence is good for lower damping and a smoother hysteresis loop. For a less smooth hysteresis loop and/or higher damping, convergence is observed to be roughly linear on average. Encouragingly, the time step needed for stability is much larger than the time period of the highest natural frequency of the structural model. Subsequently, data from several simulations conducted using the above semi-implicit method are used to construct reduced order models of the system, where the structural dynamics is projected onto a small number of modes and the number of hysteretic states is reduced significantly as well. Convergence studies of error against the number of retained hysteretic states show very good results

Reassessing the Restorative Prospectives of the King of Spices Black Pepper

Since ages, spices have been a crucial portion of human diets and trade. The bioactive principles in attendance are of noteworthy merit due to their advantageous probable against an array of disorders. Black pepper, amid piperine as its foremost element, holds affluent phytochemistry and also incorporates a number other important compounds like alkaloids, volatile oils and oleoresins. Piper nigrum is an imperative welfare spice owed to its anti-carcinogenic, antimicrobial, antioxidant apparent and gastro-defensive workings. Piperine also show evidence of speckled pharmacological characteristics like antidepressant, anti-inflammative, immunomodulatory, anticonvulsant, antihypertensive, antitumor, anti-tussive, pain reducing, antidiarrheal, antispasmodic, and cholesterol worsening . Piperine augments bioavailability of quite a few drugs and nutrients by restraining a variety of metabolising enzymes. This review is aimed to provide restructured information in recent progression of pharmacognosy, chemistry and pharmacological behavior of this miraculous King of Spices. Keywords: Black Pepper, Piperine, Antioxidant, Bioavailability, King of Spice