Numerical valuation of two-asset options under jump diffusion models using Gauss-Hermite quadrature

In this work a finite difference approach together with a bivariate Gauss–Hermite quadrature technique is developed for partial integro-differential equations related to option pricing problems on two underlying asset driven by jump-diffusion models. Firstly, the mixed derivative term is removed using a suitable transformation avoiding numerical drawbacks such as slow convergence and inaccuracy due to the appearance of spurious oscillations. Unlike the more traditional truncation approach we use 2D Gauss–Hermite quadrature with the additional advantage of saving computational cost. The explicit finite difference scheme becomes consistent, conditionally stable and positive. European and American option cases are treated. Numerical results are illustrated and analysed with experiments and comparisons with other well recognized methods.FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) Ministerio de Economía y Competitividad Spanish grant MTM2013-41765-

On the Geometry of Equiform Normal Curves in the Galilean Space G4

In our article, we establish the definition of the Equiform Normal curves in Galilean space G4. To obtain the position vector of an Equiform Normal curve in G4, we have to solve an integro-differential equation in μ2, where μ2 is the position function of a space curve γ (σ ) in the direction of third vector V3 of the Galilean space. Special cases of Equiform Normal curvatures are discussed. Finally, we prove that there is no equiform normal curve that is congruent to an Equiform Normal curve in G4

Target Detection in a Known Number of Intervals Based on Cooperative Search Technique

Finding hidden/lost targets in a broad region costs strenuous effort and takes a long time. From a practical view, it is convenient to analyze the available data to exclude some parts of the search region. This paper discusses the coordinated search technique of a one-dimensional problem with a search region consisting of several mutual intervals. In other words, if the lost target has a probability of existing in a bounded interval, then the successive bounded interval has a far-fetched probability. Moreover, the search domain is swept by two searchers moving in opposite directions, leading to three categories of target distribution truncations: commensurate, uneven, and symmetric. The truncated probability distributions are defined and applied based on the proposed classification to calculate the expected value of the elapsed time to find the hidden object. Furthermore, the optimization of the associated expected time values of various cases is investigated based on Newton's method. Several examples are presented to discuss the behavior of various distributions under each case of truncation. Also, the associated expected time values are calculated as their minimum values.Comment: 32 pages, 11 figure

Numerical valuation of two-asset options under jump diffusion models using Gauss-Hermite quadrature

In this work a finite difference approach together with a bivariate Gauss-Hermite quadrature technique is developed for partial-integro differential equations related to option pricing problems on two underlying asset driven by jump-diffusion models. Firstly, the mixed derivative term is removed using a suitable transformation avoiding numerical drawbacks such as slow convergence and inaccuracy due to the appearance of spurious oscillations. Unlike the more traditional truncation approach we use 2D Gauss-Hermite quadrature with the additional advantage of saving computational cost. The explicit finite difference scheme becomes consistent, conditionally stable and positive. European and American option cases are treated. Numerical results are illustrated and analyzed with experiments and comparisons with other well recognized methods.This work has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economía y Competitividad Spanish grant MTM2013-41765-P

Azides in the Synthesis of Various Heterocycles

In this review, we focus on some interesting and recent examples of various applications of organic azides such as their intermolecular or intramolecular, under thermal, catalyzed, or noncatalyzed reaction conditions. The aforementioned reactions in the aim to prepare basic five-, six-, organometallic heterocyclic-membered systems and/or their fused analogs. This review article also provides a report on the developed methods describing the synthesis of various heterocycles from organic azides, especially those reported in recent papers (till 2020). At the outset, this review groups the synthetic methods of organic azides into different categories. Secondly, the review deals with the functionality of the azido group in chemical reactions. This is followed by a major section on the following: (1) the synthetic tools of various heterocycles from the corresponding organic azides by one-pot domino reaction; (2) the utility of the chosen catalysts in the chemoselectivity favoring C−H and C-N bonds; (3) one-pot procedures (i.e., Ugi four-component reaction); (4) nucleophilic addition, such as Aza-Michael addition; (5) cycloaddition reactions, such as [3+2] cycloaddition; (6) mixed addition/cyclization/oxygen; and (7) insertion reaction of C-H amination. The review also includes the synthetic procedures of fused heterocycles, such as quinazoline derivatives and organometal heterocycles (i.e., phosphorus-, boron- and aluminum-containing heterocycles). Due to many references that have dealt with the reactions of azides in heterocyclic synthesis (currently more than 32,000), we selected according to generality and timeliness. This is considered a recent review that focuses on selected interesting examples of various heterocycles from the mechanistic aspects of organic azides

Novel Pyridinium Based Ionic Liquid Promoter for Aqueous Knoevenagel Condensation: Green and Efficient Synthesis of New Derivatives with Their Anticancer Evaluation

Herein, a distinctive dihydroxy ionic liquid ([Py-2OH]OAc) was straightforwardly assembled from the sonication of pyridine with 2-chloropropane-1,3-diol by employing sodium acetate as an ion exchanger. The efficiency of the ([Py-2OH]OAc as a promoter for the sono-synthesis of a novel library of condensed products through DABCO-catalyzed Knoevenagel condensation process of adequate active cyclic methylenes and ninhydrin was next investigated using ultimate greener conditions. All of the reactions studied went cleanly and smoothly, and the resulting Knoevenagel condensation compounds were recovered in high yields without detecting the aldol intermediates in the end products. Compared to traditional strategies, the suggested approach has numerous advantages including mild reaction conditions with no by-products, eco-friendly solvent, outstanding performance in many green metrics, and usability in gram-scale synthesis. The reusability of the ionic liquid was also studied, with an overall retrieved yield of around 97% for seven consecutive runs without any substantial reduction in the performance. The novel obtained compounds were further assessed for their in vitro antitumor potential toward three human tumor cell lines: Colo-205 (colon cancer), MCF-7 (breast cancer), and A549 (lung cancer) by employing the MTT assay, and the findings were evaluated with the reference Doxorubicin. The results demonstrated that the majority of the developed products had potent activities at very low doses. Compounds comprising rhodanine (5) or chromane (12) moieties exhibited the most promising cytotoxic effects toward three cell lines, particularly rhodanine carboxylic acid derivative (5c), showing superior cytotoxic effects against the investigated cell lines compared to the reference drug. Furthermore, automated docking simulation studies were also performed to support the results obtained

Positive finite difference schemes for a partial integro-differential option pricing model

[EN] This paper provides a numerical analysis for European options under partial integro-differential Bates model. An explicit finite difference scheme has been used for the differential part, while the integral part has been approximated using the four-points open type formula. The stability and consistency have been studied. Moreover, conditions guaranteing positivity of the solutions are provided. Illustrative numerical examples are included.This work has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economia y Competitividad Spanish grant MTM2013-41765-P.Fakharany, M.; Company Rossi, R.; Jódar Sánchez, LA. (2014). Positive finite difference schemes for a partial integro-differential option pricing model. Applied Mathematics and Computation. 249:320-332. https://doi.org/10.1016/j.amc.2014.10.064S32033224