Convergence of Estimated Option Price in a Regime switching Market

In an observed generalized semi-Markov regime, estimation of transition rate of regime switching leads towards calculation of locally risk minimizing option price. Despite the uniform convergence of estimated step function of transition rate, to meet the existence of classical solution of the modified price equation, the estimator is approximated in the class of smooth functions and furthermore, the convergence is established. Later, the existence of the solution of the modified price equation is verified and the point-wise convergence of such approximation of option price is proved to answer the tractability of its application in Finance. To demonstrate the consistency in result a numerical experiment has been reported.Comment: 11 pages, 2 figure

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

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

Risk Sensitive Portfolio Optimization in a Jump Diffusion Model with Regimes

This article studies a portfolio optimization problem, where the market consisting of several stocks is modeled by a multi-dimensional jump-diffusion process with age-dependent semi-Markov modulated coefficients. We study risk sensitive portfolio optimization on the finite time horizon. We study the problem by using a probabilistic approach to establish the existence and uniqueness of the classical solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation. We also implement a numerical scheme to investigate the behavior of solutions for different values of the initial portfolio wealth, the maturity, and the risk of aversion parameter.Comment: 29 pages, 3 figure

Thermodynamic properties of ultracold Bose gas: transition exponents and universality

We report exact numerical calculation of chemical potential, condensate fraction and specific heat of $N$ non-interacting bosons confined in an isotropic harmonic oscillator trap in one, two and three dimensions, as also for interacting bosons in a 3D trap. Quasi phase transitions are observed in all these cases, including one-dimension, as shown by a rapid change of all the thermodynamic quantities at the transition point. The change becomes more rapid as $N$ increases in 2D and 3D cases. However with increase in $N$, the sudden change in the nature of specific heat, gets gradually wiped out in 1D, while it becomes more drastic in 2D and 3D. The sudden change in the nature of condensate fraction and chemical potential as $N$ increases becomes more drastic even in 1D. Defining transition exponents, which characterize the nature of a thermodynamic quantity at the transition point of a quasi phase transition, we evaluate them by careful numerical calculation very near the transition temperature. These exponents are found to be independent of the size of the system and whether the bosons are interacting or not, demonstrating their universality property.Comment: The final publication is available at springerlink.co

Behavior of heat capacity of an attractive Bose-Einstein Condensate approaching collapse

We report calculation of heat capacity of an attractive Bose-Einstein condensate, with the number N of bosons increasing and eventually approaching the critical number Ncr for collapse, using the correlated potential harmonics (CPH) method. Boson pairs interact via the realistic van der Waals potential. It is found that the transition temperature Tc increases initially slowly, then rapidly as N becomes closer to Ncr . The peak value of heat capacity for a fixed N increases slowly with N, for N far away from Ncr . But after reaching a maximum, it starts decreasing when N approaches Ncr . The effective potential calculated by CPH method provides an insight into this strange behavior.Comment: 9 pages, 7 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