The aim of this paper is to price power option with its underlying asset price following exponential normal inverse gaussian (NIG) process. We first find the risk neutral equivalent martingale measure Q by Esscher transform. Then, using the Fourier transform and its inverse, we derive the analytical pricing formulas of power options which are expressed in the form of Fourier integral. In addition, the fast Fourier transform (FFT) algorithm is applied to calculate these pricing formulas. Finally, Shangzheng 50ETF options are chosen to test our results. Estimating the parameters in NIG process by maximum likelihood method, we show that the NIG prices are much closer to market prices than the Black-Scholes-Merton (BSM) ones.
In this paper, we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach. We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines, and derive all possible phase portraits under corresponding parameter conditions. Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions. The exact explicit expressions of two peakons are given. Besides, we also derive smooth solitary wave solutions, periodic wave solutions, compacton solutions, and kink-like (antikink-like) solutions. Numerical simulations are further performed to verify the correctness of the results. Most importantly, peakons and periodic cusp wave solutions are newly found for the equation, which extends the previous results.
In this paper, we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant. We prove that if the scalar curvature is not less than the Yamabe invariant in the distributional sense, then the manifold must be isometric to an Einstein manifold. This result extends Theorem 1.4 in Jiang, Sheng and Zhang [27], from a special case where the manifolds have zero Yamabe invariant to general cases where the manifolds have non-positive Yamabe invariant.
In this paper, we will discuss the almost global existence result for d-dimensional fractional nonlinear Schrödinger equation on flat torus, which is based on BNF technique, the tame property and the analysis of the spectrum of (−Δ)s.
In this paper, we prove the uniform regularity estimates for the Navier-StokesFourier system in T~n.
This paper is devoted to the existence results for a class of neutral abstract fractional differential equations involving the composite relaxation process. Based on the Laplace transform, the semigroup theory and the Wright functions, we first introduce a definition of mild solutions to the considered problem. By means of the noncompactness of measure and the fixed point technique, we establish existence criteria of solutions. Finally, an example is presented to illustrate our main result.
This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters. We consider the refuge concept of prey, which is proportional to the density of prey species with interval parameters. The model develops with natural interval parameters since the uncertainties of parameters of any ecological system are a widespread phenomenon in nature. The equilibria of the model are obtained, and the dynamic behaviours of the proposed system are examined. Simulations of the model are performed for different parameters of the model. Numerical simulations show that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature. Our study, through analytical derivation and numerical example, presents the effect of refuge on population dynamics under imprecise biological parameters.
We introduce a new generalization of the exponentiated power Lindley distribution, called the exponentiated power Lindley power series (EPLPS) distribution. The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The distribution exhibits decreasing, increasing, unimodal and bathtub shaped hazard rate functions, depending on its parameters. Several properties of the EPLPS distribution are investigated. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Finally, applications to three real data sets show the flexibility and potentiality of the EPLPS distribution.
By using a certain hybrid-type convolution operator, we first introduce a new subclass of normalized analytic functions in the open unit disk. For members of this analytic function class, we then derive several properties and characteristics including (for example) the modified Hadamard products, Hölder’s inequalities and convolution properties as well as some closure properties under a general family of integral transforms.
For the new subclass B of the bi-univalent functions constructed with the help of the (u, v)-Chebyshev polynomials of the second type, we get estimates for the first two initial coefficients and upper bounds of the Fekete-Szegő functional.
This paper investigates an international optimal investmentCconsumption problem under a random time horizon. The investor may allocate wealth between a domestic bond and an international real project with production output, whose price may exhibit discontinuities. The model incorporates the effects of taxation and exchange rate dynamics, where the exchange rate follows a stochastic differential equation with jump-diffusion. The investor’s objective is to maximize the utility of consumption and terminal wealth over an uncertain investment horizon. It is worth noting that, under our framework, the exit time is not assumed to be a stopping time. In particular, for the case of constant relative risk aversion (CRRA), we derive the optimal investment and consumption strategies by applying the separation method to solve the associated HamiltonCJacobiCBellman (HJB) equation. Moreover, several numerical examples are provided to illustrate the practical applicability of the proposed results.
Since its inception, the epsilon distribution has piqued the interest of statisticians. It has been successfully used to solve a variety of statistical problems. In this article, we propose to use the quadratic rank transmutation map mechanism to extend this distribution. This mechanism is not new; it was already used to improve the modeling capabilities of a number of existing distributions. For the original epsilon distribution, we expect the same benefits. As a result, we implement the transmuted epsilon distribution as a flexible three-parameter distribution with a bounded domain. We demonstrate its key features, focusing on the properties of its distributional mechanism and conducting quantile and moment analyses. Applications of the model are presented using two data sets. We also perform a regression analysis based on this distribution.
The main purpose of this paper is to use the Chelyshkov-collocation spectral method for solving nonlinear Quadratic integral equations of Volterra type. The method is based on the approximate solutions in terms of Chelyshkov polynomials with unknown coefficients. The Chelyshkov polynomials and their properties are employed to derive the operational matrices of integral and product. The application of these operational matrices for solving the mentioned problem is explained. The error analysis of the proposed method is investigated. Finally, some numerical examples are provided to demonstrate the efficiency of the method.
The existence and uniqueness of the maximum likelihood estimator (MLE) of parameter for the exponential-Poisson distribution is discussed by Kuş [2007. A new lifetime distribution. Computational Statistics and Data Analysis 51(9): 4497–4509] in simple random sampling (SRS). As an alternative to the MLEs in SRS, Joukar et al. [2021. Parameter estimation for the exponential-poisson distribution based on ranked set samples. Communication in Statistics-Theory and Methods 50(3): 560–581] discussed the MLE of parameter for this distribution in ranked set sampling (RSS). However, they did not discuss the existence and uniqueness of the MLE in RSS and did not provide explicit expressions for the Fisher information in RSS. In this article, we discuss the existence and uniqueness of the MLE of parameter in RSS and give explicit expressions for the Fisher information in RSS. The MLEs will be compared in terms of asymptotic efficiencies. Numerical studies and a real data application show that these MLEs in RSS can be real competitors for those in SRS.
A family of neural networks is proposed to solve linear complementarity problems (LCP). The neural networks are constructed from the novel equivalent model of LCP, which is reformulated by utilizing the modulus and smoothing technologies. Some important properties of the proposed novel equivalent model are summarized. In addition, the stability properties of the proposed steepest descent-based neural networks for LCP are analyzed. In order to illustrate the theoretical results, we provide some numerical simulations and compare the proposed neural networks with existing neural networks based on the NCP-functions. Numerical results indicate that the performance of the proposed neural networks is effective and robust.
In this paper, a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS), differential evolutionary(DE) optimization principles, and evidential reasoning(ER) methodology. The proposed approach uses q-RLDFS in order to represent the evaluating values of the alternatives corresponding to the attributes. DE optimization is used to obtain the optimal weights of the attributes, and ER methodology is used to compute the aggregated q-rung linear diophantine fuzzy values(q-RLDFVs) of each alternative. Then the score values of alternatives are computed based on the aggregated q-RLDFVs. An alternative with the maximum score value is selected as a better one. The applicability of the proposed approach has been illustrated in COVID-19 emergency decision-making system and sustainable energy planning management. Moreover, we have validated the proposed approach with a numerical example. Finally, a comparative study is provided with the existing models, where the proposed approach is found to be robust to perform better and consistent in uncertain environments.
In this study, we investigate a variety of exact soliton solutions of general (2 + 1)-dimensional Bogoyavlensky-Konopelchenko equation via the exp(−Φ(η))-expansion method and modified Kudryashov method. The exact solutions are characterized in the form of hyperbolic, trigonometric and rational function solutions using exp(−Φ(η))-expansion method, whereas the solution in the form of hyperbolic function expression is obtained by the modified Kudryashov method. These exact solutions also include kink, bright, dark, singular and periodic soliton solutions. The graphical interpretation of the exact solutions is addressed for specific choices of the parameters appearing in the solutions.
A promising avenue to control mosquito-borne diseases such as dengue, malaria,and Zika involves releasing male mosquitoes carrying the bacterium Wolbachia in wild areas to drive female sterility by a mechanism called cytoplasmic incompatibility(CI). In this work,we initiate a preliminary assessment of how the combined impact of dispersal, incomplete CI and mating competitiveness on mosquito population suppression by a delay differential equation model. Our theoretical analyses indicate that the immigration of eggs plays a significant role in the suppression dynamics. For the case without egg immigration, we identify a threshold dispersal rate v*of adult mosquitoes, threshold CI density ξ*, and threshold release ratio r*. A successful mosquito suppression would be established only when v < v*, ξ > ξ*, and r(t) ≥ r*uniformly. The immigration of eggs causes the threshold dynamics to be invalid, and warns an absolute failure of population suppression. The monotonicity of the adult steady-state in the dispersal rate and CI intensity indicates that choosing a suitable Wolbachia strain with strong CI intensity, or bringing down the dispersal rate of mosquitoes by blocking the suppression zones is a feasible strategy to obtain a better suppression level.
This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain. It is shown that the system possesses a globally bounded solution under some conditions.
In this paper, the nonlinear Schrödinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.
