Discounted optimal stopping of a Brownian bridge, with application to American options under pinning

Mathematically, the execution of an American-style financial derivative is commonly reduced to solving an optimal stopping problem. Breaking the general assumption that the knowledge of the holder is restricted to the price history of the underlying asset, we allow for the disclosure of future information about the terminal price of the asset by modeling it as a Brownian bridge. This model may be used under special market conditions, in particular we focus on what in the literature is known as the "pinning effect", that is, when the price of the asset approaches the strike price of a highly-traded option close to its expiration date. Our main mathematical contribution is in characterizing the solution to the optimal stopping problem when the gain function includes the discount factor. We show how to numerically compute the solution and we analyze the effect of the volatility estimation on the strategy by computing the confidence curves around the optimal stopping boundary. Finally, we compare our method with the optimal exercise time based on a geometric Brownian motion by using real data exhibiting pinning.Comment: 29 pages, 9 figures. Supplementary material: 5 R scripts, 4 RData file

Analysing the effects of sugar sweetened beverages' tax

Treball Final de Grau en Economia. Codi: EC1049. Curs acadèmic: 2016/2017This research tries to analyse the effects that tax on sugar sweetened beverages have on population’s health. Based on several investigations it is argued the relation found between high sugar intake and obesity, type 2 diabetes and other non-communicable diseases. It has been observed that this usually affect more notoriously children and young people than adults. It is estimated capability of the tax to reduce notably the consumption of this product due to a price elasticity close to the unity. It is also observed the behaviour of the demand and the effects that has had on health the introduction of the tax in others in other countries. The aim of this research is to examine the previous literature about sugar sweetened beverages taxation, the potential impact on its intake and the consequent reduction of overweigh, obesity and other non-communicable diseases

La capilla de San Marcos, castillo de Bellver (Mallorca): una nueva hipótesis sobre su pavimento

Resumen:El presente estudio aporta información poco conocida de la capilla del Castillo de Bellver, en Palma de Mallorca, feudo que ha suscitado no poca curiosidad dentro del ámbito de la castellología. Contiene en su interior una capilla en la que se presupone los reyes de la dinastía real mallorquina realizaban sus actividades de culto durante sus estancias en este recinto de recreo. Resulta de especial interés el pavimento de su presbiterio, sobre el que tratamos de aportar algunos datos para sugerirle una cronología adecuada.Resum:La capella de Sant Marc, castell de Bellver (Mallorca): una nova hipòtesi sobre el seu pavimentEl present estudi aporta informació sobre la capella del Castell de Bellver, a Palma de Mallorca, un emplaçament que ha suscitat la no poca curiositat dins l’àmbit de la castellologia. Conté al seu interior una capella que es pressuposa era on els reis de la dinastia mallorquina realitzaven les tasques del culte durant les seves estances dins d’aquest recinte d’esbarjo. És d’especial interés el paviment del presbiteri, sobre el qual s’intentarà deduïr algunes dades per tal de proposar una cronología adequada.Abstract:The Saint Mark’s Chapel in Bellver Castle, Palma de Mallorca: a new hypothesis about their pavementThis work is a short study of the Bellver’s Castle Chapel, in Palma de Mallorca. This singular building arouses the curiosity of all students of Castleology. It has inside its walls a small chapel where, presumably, the kings of Majorca performed the rituals of their cult during their stay here. The altar pavement of this shrine is very interesting, and we want to date it accurately

Accidental displacement and migration of endosseous implants into adjacent craniofacial structures : a review and update

Objectives: Accidental displacement of endosseous implants into the maxillary sinus is an unusual but potential complication in implantology procedures due to the special features of the posterior aspect of the maxillary bone; there is also a possibility of migration throughout the upper paranasal sinuses and adjacent structures. The aim of this paper is to review the published literature about accidental displacement and migration of dental implants into the maxillary sinus and other adjacent structures. Study D esign: A review has been done based on a search in the main on-line medical databases looking for papers about migration of dental implants published in major oral surgery, periodontal, dental implant and ear-nose- throat journals, using the keywords ?implant,? ?migration,? ?complication,? ?foreign body? and ?sinus.? Results: 24 articles showing displacement or migration to maxillary, ethmoid and sphenoid sinuses, orbit and cranial fossae, with different degrees of associated symptoms, were identified. Techniques found to solve these clinical issues include Cadwell-Luc approach, transoral endoscopy approach via canine fossae and transnasal functional endoscopy surgery. Conclusion: Before removing the foreign body, a correct diagnosis should be done in order to evaluate the functional status of the ostiomeatal complex and the degree of affectation of paranasal sinuses and other involved structures, determining the size and the exact location of the foreign body. After a complete diagnosis, an indicated procedure for every case would be decide

Split and Shift Methodology: Overcoming Hardware Limitations on Cellular Processor Arrays for Image Processing

Na era multimedia, o procesado de imaxe converteuse nun elemento de singular importancia nos dispositivos electrónicos. Dende as comunicacións (p.e. telemedicina), a seguranza (p.e. recoñecemento retiniano) ou control de calidade e de procesos industriais (p.e. orientación de brazos articulados, detección de defectos do produto), pasando pola investigación (p.e. seguimento de partículas elementais) e diagnose médica (p.e. detección de células estrañas, identificaciónn de veas retinianas), hai un sinfín de aplicacións onde o tratamento e interpretación automáticas de imaxe e fundamental. O obxectivo último será o deseño de sistemas de visión con capacidade de decisión. As tendencias actuais requiren, ademais, a combinación destas capacidades en dispositivos pequenos e portátiles con resposta en tempo real. Isto propón novos desafíos tanto no deseño hardware como software para o procesado de imaxe, buscando novas estruturas ou arquitecturas coa menor area e consumo de enerxía posibles sen comprometer a funcionalidade e o rendemento

Further Results on the Total Roman Domination in Graphs

[EN] Let G be a graph without isolated vertices. A function f:V(G)-> {0,1,2} is a total Roman dominating function on G if every vertex v is an element of V(G) for which f(v)=0 is adjacent to at least one vertex u is an element of V(G) such that f(u)=2 , and if the subgraph induced by the set {v is an element of V(G):f(v)>= 1} has no isolated vertices. The total Roman domination number of G, denoted gamma tR(G) , is the minimum weight omega (f)=Sigma v is an element of V(G)f(v) among all total Roman dominating functions f on G. In this article we obtain new tight lower and upper bounds for gamma tR(G) which improve the well-known bounds 2 gamma (G)<= gamma tR(G)<= 3 gamma (G) , where gamma (G) represents the classical domination number. In addition, we characterize the graphs that achieve equality in the previous lower bound and we give necessary conditions for the graphs which satisfy the equality in the upper bound above.Cabrera Martínez, A.; Cabrera García, S.; Carrión García, A. (2020). Further Results on the Total Roman Domination in Graphs. Mathematics. 8(3):1-8. https://doi.org/10.3390/math8030349S1883Henning, M. A. (2009). A survey of selected recent results on total domination in graphs. Discrete Mathematics, 309(1), 32-63. doi:10.1016/j.disc.2007.12.044Henning, M. A., & Yeo, A. (2013). Total Domination in Graphs. Springer Monographs in Mathematics. doi:10.1007/978-1-4614-6525-6Henning, M. A., & Marcon, A. J. (2016). Semitotal Domination in Claw-Free Cubic Graphs. Annals of Combinatorics, 20(4), 799-813. doi:10.1007/s00026-016-0331-zHenning, M. . A., & Marcon, A. J. (2016). Vertices contained in all or in no minimum semitotal dominating set of a tree. Discussiones Mathematicae Graph Theory, 36(1), 71. doi:10.7151/dmgt.1844Henning, M. A., & Pandey, A. (2019). Algorithmic aspects of semitotal domination in graphs. Theoretical Computer Science, 766, 46-57. doi:10.1016/j.tcs.2018.09.019Cockayne, E. J., Dreyer, P. A., Hedetniemi, S. M., & Hedetniemi, S. T. (2004). Roman domination in graphs. Discrete Mathematics, 278(1-3), 11-22. doi:10.1016/j.disc.2003.06.004Stewart, I. (1999). Defend the Roman Empire! Scientific American, 281(6), 136-138. doi:10.1038/scientificamerican1299-136Chambers, E. W., Kinnersley, B., Prince, N., & West, D. B. (2009). Extremal Problems for Roman Domination. SIAM Journal on Discrete Mathematics, 23(3), 1575-1586. doi:10.1137/070699688Favaron, O., Karami, H., Khoeilar, R., & Sheikholeslami, S. M. (2009). On the Roman domination number of a graph. Discrete Mathematics, 309(10), 3447-3451. doi:10.1016/j.disc.2008.09.043Liu, C.-H., & Chang, G. J. (2012). Upper bounds on Roman domination numbers of graphs. Discrete Mathematics, 312(7), 1386-1391. doi:10.1016/j.disc.2011.12.021González, Y., & Rodríguez-Velázquez, J. (2013). Roman domination in Cartesian product graphs and strong product graphs. Applicable Analysis and Discrete Mathematics, 7(2), 262-274. doi:10.2298/aadm130813017gLiu, C.-H., & Chang, G. J. (2012). Roman domination on strongly chordal graphs. Journal of Combinatorial Optimization, 26(3), 608-619. doi:10.1007/s10878-012-9482-yAhangar Abdollahzadeh, H., Henning, M., Samodivkin, V., & Yero, I. (2016). Total Roman domination in graphs. Applicable Analysis and Discrete Mathematics, 10(2), 501-517. doi:10.2298/aadm160802017aAmjadi, J., Sheikholeslami, S. M., & Soroudi, M. (2019). On the total Roman domination in trees. Discussiones Mathematicae Graph Theory, 39(2), 519. doi:10.7151/dmgt.2099Cabrera Martínez, A., Montejano, L. P., & Rodríguez-Velázquez, J. A. (2019). Total Weak Roman Domination in Graphs. Symmetry, 11(6), 831. doi:10.3390/sym1106083

Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures

Let μ be a probability measure on T that is singular with respect to the Haar measure. In this paper we study Fourier expansions in L2(T,μ) using techniques from the theory of model subspaces of the Hardy space. Since the sequence of monomials {zn}n∈N is effective in L2(T,μ), it has a Parseval frame associated via the Kaczmarz algorithm. Our first main goal is to identify the aforementioned frame with boundary values of the frame Pφ(zn) for the model subspace H(φ)=H2⊖φH2, where Pφ is the orthogonal projection from the Hardy space H2 onto H(φ). The study of Fourier expansions in L2(T,μ) also leads to consider positive kernels in the Hardy space. Our second main goal is to study the set of measures μ which reproduce a kernel contained in a model subspace. We completely characterize this set when the kernel is the reproducing kernel of a model subspace, and we study the consequences of this characterization.Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; ArgentinaFil: García, María Guadalupe. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentin

Distracción osteogénica del reborde alveolar: revisión de la literatura

Uno de los principales problemas para la colocación de implantes dentales es la presencia de hueso insuficiente que impide que sean de una longitud y/o de un diámetro adecuados. Dentro de los métodos que se usan para el aumento del reborde alveolar se incluye tan solo desde hace una década la aplicación de los principios de distracción osteogénica (DO). Esta técnica se basa en la separación gradual de dos fragmentos de hueso perfectamente vascularizados, entre los que se forma un callo de distracción que progresivamente se transforma en hueso maduro. Un científico clave en el desarrollo de esta técnica fue el traumatólogo ruso Ilizarov. Esta revisión bibliográfica evalúa la metodología, el funcionamiento y las posibles aplicaciones de DO en el tratamiento de los defectos del reborde alveolar. Por sus cualidades demostradas, la DO podría sustituir el uso de injertos y regeneración ósea guiada para favorecer las relaciones esqueléticas de los rebordes alveolares.One of the principal problems in dental implantation is the lack of sufficient bone height or width. In the case of the alveolar ridge, a very effective technique for resolving this problem is distraction osteogenesis, introduced in this context about a decade ago. This technique is based on the gradual separation of a mobile but fully vascularized bone segment from the basal bone, leading to the formation of an intervening soft callus which gradually transforms to mature bone. A key researcher in the development of this technique was the Russian traumatologist Ilizarov. The present article reviews alveolar ridge distraction procedures and their clinical application. Alveolar ridge distraction may often be preferable to bone grafting or guided bone regeneration for increasing ridge height and width prior to implantation

Non spontaneous saccadic movements identification in clinical electrooculography using machine learning

In this paper we evaluate the use of the machine learning algorithms Support Vector Machines, K-Nearest Neighbors, CART decision trees and Naive Bayes to identify non spontaneous saccades in clinical electrooculography tests. Our approach tries to solve problems like the use of manually established thresholds present in classical methods like identification by velocity threshold (I-VT) or identification by dispersion threshold (I-DT). We propose a modification to an adaptive threshold estimation algorithm for detecting signal impulses without the need of any user input. Also, a set of features were selected to take advantage of intrinsic characteristics of clinical electrooculography tests. The models were evaluated with signals recorded to subjects affected by Spinocerebellar Ataxia type 2 (SCA2). Results obtained by the algorithm shows accuracies over 97%, recalls over 97% and precisions over 91% for the four models evaluated.Universidad de Málaga, Campus de excelencia de Andalucía Tec