Optimal hedging of Derivatives with transaction costs

We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton-Bellman-Jacobi equation, which by the verification theorem has well-behaved solutions if certain conditions on a potential are satisfied. In the case at hand, these conditions simply imply arbitrage-free ("Black-Scholes") pricing of the derivative. While pricing is hence not changed by friction allow a portfolio to fluctuate around a delta hedge. In the limit of weak friction, we determine the optimal control to essentially be of two parts: a strong control, which tries to bring the stock-and-derivative portfolio towards a Black-Scholes delta hedge; and a weak control, which moves the portfolio by adding or subtracting a Black-Scholes hedge. For simplicity we assume growth-optimal investment criteria and quadratic friction.Comment: Revised version, expanded introduction and references 17 pages, submitted to International Journal of Theoretical and Applied Finance (IJTAF

Large-scale impact of Saharan dust on the North Atlantic Ocean circulation

The potential for a dynamical impact of Saharan mineral dust on the North Atlantic Ocean large-scale circulation is investigated. To this end, an ocean general circulation model forced by atmospheric fluxes is perturbed by an idealized, seasonally varying, net shortwave flux anomaly, as it results from remote sensing observations of aerosol optical thickness representing Saharan dust load in the atmosphere. The dust dynamical impact on the circulation is assessed through a comparison between perturbed and an unperturbed run. Results suggest that, following the dust-induced shortwave irradiance anomaly, a buoyancy anomaly is created in the Atlantic offshore the African coast, which over the course of the time propagates westward into the interior Atlantic while progressively subducting. Changes in the large-scale barotropic and overturning circulations are significant after 3 years, which coincides with the elapsed time required by the bulk of the buoyancy perturbation to reach the western boundary of the North Atlantic. Although small in amplitude, the changes in the meridional overturning are of the same order as interannual-to-decadal variability. Variations in the amplitude of the forcing lead to changes in the amplitude of the response, which is almost linear during the first 3 years. In addition, a fast, but dynamically insignificant, response can be observed to propagate poleward along the eastern boundary of the North Atlantic, which contributes to a nonlinear response in the subpolar region north of 40°N

Effects of Turbulent Mixing on the Critical Behavior

Effects of strongly anisotropic turbulent mixing on the critical behavior are studied by means of the renormalization group. Two models are considered: the equilibrium model A, which describes purely relaxational dynamics of a nonconserved scalar order parameter, and the Gribov model, which describes the nonequilibrium phase transition between the absorbing and fluctuating states in a reaction-diffusion system. The velocity is modelled by the d-dimensional generalization of the random shear flow introduced by Avellaneda and Majda within the context of passive scalar advection. Existence of new nonequilibrium types of critical regimes (universality classes) is established.Comment: Talk given in the International Bogolyubov Conference "Problems of Theoretical and Mathematical Physics" (Moscow-Dubna, 21-27 August 2009

Interior comfort regulation with gypsum plasters

In this work, the performance of a manually applied thin layer of a multilayer gypsum plaster system, for interior lining of walls and ceilings, incorporating phase change materials (PCM), is investigated. The study aims the development of a passive solar storage system that can be combined with both active heating and cooling storage systems and equipments. Mechanical and thermal tests were carried in laboratory, in two test cells and in residential buildings. Results so far showed that the gypsum plaster with 20%-wt. PCM reduces up to 45-50% flexural and compressive strengths, but the specifications of the European standard for these materials are fulfil. On what concerns thermal properties, the use of gypsum-PCM plaster reduces the maximum room temperature up to 5 ºC with a time delay of 3 hours and increases the minimum room temperature up to 1.5 ºC with a time delay of 2 hours. Besides, it also reduces room relative humidity up to 10%. Power savings of 0.44 W/m2wall.m2floor were estimated, with higher potential for lower temperatures, according to tests carried in a Passy’s test cell during the cooling season.Agência de Inovação (ADI

Spectrum of the Fokker-Planck operator representing diffusion in a random velocity field

We study spectral properties of the Fokker-Planck operator that represents particles moving via a combination of diffusion and advection in a time-independent random velocity field, presenting in detail work outlined elsewhere [J. T. Chalker and Z. J. Wang, Phys. Rev. Lett. {\bf 79}, 1797 (1997)]. We calculate analytically the ensemble-averaged one-particle Green function and the eigenvalue density for this Fokker-Planck operator, using a diagrammatic expansion developed for resolvents of non-Hermitian random operators, together with a mean-field approximation (the self-consistent Born approximation) which is well-controlled in the weak-disorder regime for dimension d>2. The eigenvalue density in the complex plane is non-zero within a wedge that encloses the negative real axis. Particle motion is diffusive at long times, but for short times we find a novel time-dependence of the mean-square displacement, $\sim t^{2/d}$ in dimension d>2, associated with the imaginary parts of eigenvalues.Comment: 8 pages, submitted to Phys Rev

Malvinas-slope water intrusions on the northern Patagonia continental shelf

The Patagonia continental shelf located off southeastern South America is bounded offshore by the Malvinas Current, which extends northward from northern Drake Passage (~55° S) to nearly 38° S. The transition between relatively warm-fresh shelf waters and Subantarctic Waters from the western boundary current is characterized by a thermohaline front extending nearly 2500 km. We use satellite derived sea surface temperature, and chlorophyll-<I>a</I> data combined with hydrographic and surface drifter data to document the intrusions of slope waters onto the continental shelf near 41° S. These intrusions create vertically coherent localized negative temperature and positive salinity anomalies extending onshore about 150 km from the shelf break. The region is associated with a center of action of the first mode of non-seasonal sea surface temperature variability and also relatively high chlorophyll-<I>a</I> variability, suggesting that the intrusions are important in promoting the local development of phytoplankton. The generation of slope water penetrations at this location may be triggered by the inshore excursion of the 100 m isobath, which appears to steer the Malvinas Current waters over the outer shelf

Impacts of regional mixing on the temperature structure of the equatorial Pacific Ocean. Part 1: Vertically uniform vertical diffusion

AbstractWe investigate the sensitivity of numerical-model solutions to regional changes in vertical diffusion. Specifically, we vary the background diffusion coefficient, κb, within spatially distinct subregions of the tropical Pacific, assess the impacts of those changes, and diagnose the processes that account for them.Solutions respond to a diffusion anomaly, δκb, in three ways. Initially, there is a fast response (several months), due to the interaction of rapidly-propagating, barotropic and gravity waves with eddies and other mesoscale features. It is followed by a local response (roughly one year), the initial growth and spatial pattern of which can be explained by one-dimensional (vertical) diffusion. At this stage, temperature and salinity anomalies are generated that are either associated with a change in density (“dynamical” anomalies) or without one (“spiciness” anomalies). In a final adjustment stage, the dynamical and spiciness anomalies spread to remote regions by radiation of Rossby and Kelvin waves and by advection, respectively.In near-equilibrium solutions, dynamical anomalies are generally much larger in the latitude band of the forcing, but the impact of off-equatorial forcing by δκb on the equatorial temperature structure is still significant. Spiciness anomalies spread equatorward within the pycnocline, where they are carried to the equator as part of the subsurface branch of the Pacific Subtropical Cells, and spiciness also extends to the equator via western-boundary currents. Forcing near and at the equator generates strong dynamical anomalies, and sometimes additional spiciness anomalies, at pycnocline depths. The total response of the equatorial temperature structure to δκb in various regions depends on the strength and spatial pattern of the generation of each signal within the forcing region as well as on the processes of its spreading to the equator

Flame Enhancement and Quenching in Fluid Flows

We perform direct numerical simulations (DNS) of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain v ~ U^{1/4}. We also study flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of the size W can be typically quenched by a flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ~ W^4 if the cell size is smaller than a critical value.Comment: 14 pages, 20 figures, revtex4, submitted to Combustion Theory and Modellin

Dual-arm dexterous mobile manipulator with new omnidirectional wheels

[ES] Este artículo describe un manipulador móvil, bimanual y con capacidad de manipulación diestra denominado MADAR (de Mobile Anthropomorphic Dual-Arm Robot). Básicamente puede dividirse en dos partes, una base móvil y una estructura superior portando dos brazos en configuración antropomorfa con manos mecánicas diestras equipadas con sensores táctiles. La base, completamente de desarrollo propio, es de forma circular y tiene tres ruedas con un diseño novedoso que permiten una movilidad omnidireccional. La estructura superior integra elementos comerciales, como los brazos, las manos y distintos sensores, que han sido adaptados para su funcionamiento conjunto. El artículo incluye tanto la descripción de los principales elementos del hardware como del software desarrollado para su control y uso.[EN] This article describes a mobile manipulator, equipped with two arms with dexterous capabilities, called MADAR (from Mobile Anthropomorphic Dual-Arm Robot). Basically, the manipulator can be divided into two parts, a mobile base and an upper structure that includes two arms with dexterous hands equipped with tactile sensors. The base, completely self-developed, is circular in shape and has three wheels with a novel design that allow omnidirectional mobility. The upper structure integrates commercial elements, such as the arms, the hands and dierent sensors. The article includes the description of the main elements of the hardware and the software developed for its control and use.Este trabajo ha sido parcialmente financiado por el gobierno español mediante el proyecto DPI2016-80077-R.Suárez, R.; Palomo-Avellaneda, L.; Martínez, J.; Clos, D.; García, N. (2020). Manipulador móvil, bibrazo y diestro con nuevas ruedas omnidireccionales. Revista Iberoamericana de Automática e Informática industrial. 17(1):10-21. https://doi.org/10.4995/riai.2019.11422OJS1021171ABB, Jan. 2018. YuMi. www.abb.com/yumi, visitado el 2019/02/12.Adascalitei, F., Doroftei, I., Jan. 2011. Practical applications for mobile robots based on mecanum wheels - a systematic survey. Romanian Review Precision Mechanics, Optics and Mechatronics, 21-29.Adept, Jan. 2018. Pioneer manipulator. https://www.generationrobots.com/media/PioneerManipulatordatasheet.pdf.Albu-Schöffer, A., Haddadin, S., Ott, C., Stemmer, A., Wimböck, T., Hirzinger, G., May 2007. The DLR lightweight robot: Design and control concepts for robots in human environments. Industrial Robot: An Int. J. 34 (5), 376-385. https://doi.org/10.1108/01439910710774386Andersen, T., 2015. Optimizing the Universal Robots ROS driver. Tech. rep., Technical University of Denmark, Department of Electrical Engineering.Arthur Ketels and M.J.G. van den Molengraft, 2014. Open ethercat society: Home of soem and soes. openethercatsociety.github.io, visitado el 2019/02/12.Batlle, J., Barjau, A., 2009. Holonomy in mobile robots. Robotics and Auton. Systems 57 (4), 433 - 440. https://doi.org/10.1016/j.robot.2008.06.001Batlle, J., Font-Llagunes, J., Barjau, A., Jan. 2010. Calibration for mobile robots with an invariant Jacobian. Robotics and Auton. Systems 58, 10-15. https://doi.org/10.1016/j.robot.2009.09.002Bischoff, R., Huggenberger, U., Prassler, E., May 2011. KUKA youBot - A mobile manipulator for research and education. In: Proc. IEEE Int. Conf. Robotics and Automation. pp. 1-4. https://doi.org/10.1109/ICRA.2011.5980575Bridgwater, L., A. Ihrke, C., Diftler, M., Abdallah, M., Radford, N., Rogers, J., Yayathi, S., S. Askew, R., M. Linn, D., 05 2012. The robonaut 2 handdesigned to do work with tools. In: Proceedings - IEEE International Conference on Robotics and Automation. pp. 3425-3430. https://doi.org/10.1109/ICRA.2012.6224772Butterfass, J., Fischer, M., Grebenstein, M., Haidacher, S., Hirzinger, G., 2004. Design and experiences with DLR hand II. In: Proc. of World Automation Congress. Vol. 15. pp. 105-110.Clos, D., Martı́nez, J., 2015. Omnidirectional wheel, and omnidirectional mobile device. World Intellectual Property Organization (Patent WO 2015/121521 A1, lens.org/084-354-767-767-633).Company, S. R., 2015. Shadow Robot Company. Shadow Dexterous Hand. [Online] http://www.shadowrobot.com.Dean-Leon, E., Pierce, B., Bergner, F., Mittendorfer, P., Ramirez-Amaro, K., Burger, W., Cheng, G., 2017. TOMM: Tactile omnidirectional mobile manipulator. In: Proc. IEEE Int. Conf. Robotics and Autom. pp. 2441-2447. https://doi.org/10.1109/ICRA.2017.7989284Fentanes, J. P., Zalama, E., Garc'ıa-Bermejo, J. G., 2012. Plataforma robótica para tareas de reconstrucci'on tridimensional de entornos exteriores. Revista Iberoamericana de Automática e Informática industrial 9 (1), 81-82. https://doi.org/10.1016/j.riai.2011.11.009Ferriere, L., Raucent, B., May 1998. ROLLMOBS, a new universal wheel concept. In: Proc. IEEE Int. Conf. Robotics and Automation. Vol. 3. pp. 1877-1882.Fitzgerald, C., Apr. 2013. Developing baxter. In: Proc. IEEE Int. Conf. Technologies for Practical Robot Appl. pp. 1-6. https://doi.org/10.1109/TePRA.2013.6556344Garcı́a, N., Rosell, J., Suárez, R., 2017. Motion planning by demonstration with human-likeness evaluation for dual-arm robots. IEEE Trans. Systems, Man, and Cybernetics: Systems PP (99), 1-10. https://doi.org/10.1109/TSMC.2017.2756856Gerum, P., 2004. Xenomai-Implementing a RTOS emulation framework on GNU/Linux. https://xenomai.org/documentation/xenomai-2.1/pdf/xenomai.pdf, visitado el 2019/05/31.Hermann, A., Sun, J., Xue, Z., Rühl, S. W., Oberländer, J., Roennau, A., Zöllner, J. M., Dillmann, R., July 2013. Hardware and software architecture of the bimanual mobile manipulation robot hollie and its actuated upper body. In: 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM). Wollongong, NSW, Australia, pp. 286-292. https://doi.org/10.1109/AIM.2013.6584106IOC Robotics Lab, 2014. SOEM for RTNET and Xenomai. github.com/iocroblab/soem, visitado el 2019/02/12.Khatib, O., 1999. Mobile manipulation: The robotic as-sistant. Robotics and Auton. Systems 26 (2), 175 - 183. https://doi.org/10.1016/S0921-8890(98)00067-0Kröger, T., May 2011. Opening the door to new sensor-based robot applications - The Reflexxes Motion Libraries. In: IEEE Int. Conf. Robotics and Automation. pp. 1-4. https://doi.org/10.1109/ICRA.2011.5980578Kuka Robotics, 2018. KMR iiwa. www.kuka.com/en-us/products/mobility/mobile-robot-systems/kmr-iiwa, visitado el 2019/02/12.Kurazume, R., Hasegawa, T., Oct 2006. A new index of serial-link manipulator performance combining dynamic manipulability and manipulating force ellipsoids. IEEE Trans. Robotics 22 (5), 1022-1028. https://doi.org/10.1109/TRO.2006.878949Lind, M., Schrimpf, J., Ulleberg, T., 2010. Open real-time robot controller framework. In: Proc. CIRP Conf. Assembly Technology and Systems - Responsive, customer demand driven, adaptive assembly. pp. 13-18.Montaño, A., Suárez, R., 2015. Unknown object manipulation based on tactile information. In: IEEE/RSJ Int. Conf. Intelligent Robots and Systems. pp. 5642-5647. https://doi.org/10.1109/IROS.2015.7354178Montaño, A., Suárez, R., Oct 2018a. Improving grasping forces during the manipulation of unknown objects. In: 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). pp. 3490-3495. https://doi.org/10.1109/IROS.2018.8593655Montaño, A., Suárez, R., 2018b. Manipulation of unknown objects to improve the grasp quality using tactile information. Sensors 18 (5-1412). https://doi.org/10.3390/s18051412PAL Robotics, Jan. 2018. Tiago. tiago.pal-robotics.com, visitado el 2019/02/12.Pozyx NV, 2018. Creator Pozyx. www.pozyx.io, visitado el 2019/02/12.Quigley, M., Conley, K., Gerkey, B. P., Faust, J., Foote, T., Leibs, J., Wheeler, R., Ng, A. Y., 2009. Ros: an open-source robot operating system. In: ICRA Workshop on Open Source Software.Reitelshöfer, S., Ramer, C., Gräf, D., Matern, F., Franke, J., Dec. 2014. Combining a collaborative robot and a lightweight Jamming-Gripper to realize an intuitively to use and flexible co-worker. In: Proc. IEEE/SICE Int. Symp. System Integration. pp. 1-5. https://doi.org/10.1109/SII.2014.7028001Roa, M., Suárez, R., Cornellà, J., 2008. Medidas de calidad para la prensión de objetos. Revista Iberoamericana de Automática e Informatica Industrial, RIAI 5 (1), 66-82. https://doi.org/10.1016/S1697-7912(08)70124-9Rojas-de-Silva, A., Suárez, R., 2016. Grasping bulky objects with two anthropomorphic hands. In: IEEE/RSJ Int. Conf. Intelligent Robots and Systems. pp. 877-884. https://doi.org/10.1109/IROS.2016.7759154ROS-I Consortium, 2012. ROS-Industrial. rosindustrial.org/, visitado el 2019/02/12.Rosell, J., Pérez, A., Aliakbar, A., Muhayyuddin, Palomo, L., Garcı́a, N., Sept. 2014. The Kautham Project: A teaching and research tool for robot motion planning. In: Proc. IEEE Int. Conf. Emerging Technologies and Factory Automation. https://doi.org/10.1109/ETFA.2014.7005143Runge, G., Borchert, G., Raatz, A., Sept 2014. Design of a holonomic ball drive for mobile robots. In: Proc. IEEE/ASME Int. Conf. Mechatronic and Embedded Systems and Applications. pp. 1-6. https://doi.org/10.1109/MESA.2014.6935568Sadun, A. S., Jalani, J., Jamil, F., Sep. 2016. Grasping analysis for a 3-finger adaptive robot gripper. In: 2016 2nd IEEE International Symposium on Robotics and Manufacturing Automation (ROMA). pp. 1-6. https://doi.org/10.1109/ROMA.2016.7847806SCHUNK GmbH, 2011. Shunk dexterous hand - SDH2. schunk.com/us_en/gripping-systems/series/sdh/, visitado el 2019/02/12.SICK Vertriebs-GmbH, 2018. TiM5xx. www.sick.com/de/en/detection-and-ranging-solutions/2d-lidar-sensors/tim5xx/tim561-2050101/p/p369446, visitado el 2019/02/12.SimLab-Wonik Robotics, Set. 2012. Allegro hand is a low-cost and highly adaptive robotic hand. www.simlab.co.kr/Allegro-Hand.htm, visitadoel 2019/02/12.Suárez, R., Grosch, P., Jul 2004. Dexterous robotic hand ma-i, sofware and hardware architecture. In: Intelligent Manipulation and Grasping International Conference, IMG'04. pp. 91-96.Suárez, R., Rosell, J., Garcı́a, N., May 2015. Using synergies in dual-arm manipulation tasks. In: Proc. IEEE Int. Conf. Robotics and Automation. pp. 5655-5661. https://doi.org/10.1109/ICRA.2015.7139991Suárez, R., Palomo-Avellaneda, L., Martinez, J., Clos, D., Garcı́a, N., 2018.Development of a dexterous dual-arm omnidirectional mobile manipulator. IFAC-PapersOnLine 51 (22), 126 - 131, 12th IFAC Symposium on Robot Control SYROCO 2018. https://doi.org/10.1016/j.ifacol.2018.11.529SYNTENET, 2014. Projecto: Sincronización y teleoperación con interacción visual 3d de redes de manipuladores móviles y robots con articulaciones flexibles. Referencia: DPI2011-22471, Perido: 01/01/2012 al 31/12/2014, IP: Luis Basañez, IOC-UPC.Universal Robots, Feb. 2019. Ur5 collaborative robot arm. www.universal-robots.com/products/ur5-robot, visitado el 2019/02/12.Weiss Robotics, 2015. WTS-FT; Weiss Robotics GmbH&Co.KG. www.weiss-robotics.com/en/produkte/tactile-sensing/wts-ft-en/, visitado el 2019/02/12.Willow Garage, 2010. Willow Garage PR2. http://www.willowgarage.com/pages/pr2/overview, visitado el 2019/06/06

Nonlinear Parabolic Equations arising in Mathematical Finance

This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387