249 research outputs found
Meshfree Approximation for Multi-Asset Options
No full textWe price multi-asset options by solving their price partial differential equations using a meshfree approach with radial basis functions under jump-diffusion and geometric Brownian motion frameworks. In the geometric Brownian motion framework, we propose an effective technique that breaks the multi-dimensional problem to multiple 3D problems. We solve the price PDEs or PIDEs with an implicit meshfree scheme using thin-plate radial basis functions. Meshfree approach is very accurate, has high order of convergence and is easily scalable and adaptable to higher dimensions and different payoff profiles. We also obtain closed form approximations for the option Greeks. We test the model on American crack spread options traded on NYMEX.Multi-asset options, radial basis function, meshfree approximation, collocation, multidimensional Lévy process, basket options, PIDE, PDE
On the numerical solution of space–time fractional diffusion models
No full textA flexible numerical scheme for the discretization of the space–time fractional diffusion equation is pre- sented. The model solution is discretized in time with a pseudo-spectral expansion of Mittag–Leffler functions. For the space discretization, the proposed scheme can accommodate either low-order finite- difference and finite-element discretizations or high-order pseudo-spectral discretizations. A number of examples of numerical solutions of the space–time fractional diffusion equation are presented with various combinations of the time and space derivatives. The proposed numerical scheme is shown to be both efficient and flexible
Predicting the cumulative effect of multiple disturbances on seagrass connectivity
No full textThe rate of exchange, or connectivity, among populations effects their ability to recover after disturbance events. However, there is limited information on the extent to which populations are connected or how multiple disturbances affect connectivity, especially in coastal and marine ecosystems. We used network analysis and the outputs of a biophysical model to measure potential functional connectivity and predict the impact of multiple disturbances on seagrasses in the central Great Barrier Reef World Heritage Area (GBRWHA), Australia. The seagrass networks were densely connected, indicating that seagrasses are resilient to the random loss of meadows. Our analysis identified discrete meadows that are important sources of seagrass propagules and that serve as stepping stones connecting various different parts of the network. Several of these meadows were close to urban areas or ports and likely to be at risk from coastal development. Deep water meadows were highly connected to coastal meadows and may function as a refuge, but only for non-foundation species. We evaluated changes to the structure and functioning of the seagrass networks when one or more discrete meadows were removed due to multiple disturbance events. The scale of disturbance required to disconnect the seagrass networks into two or more components was on average >245 km, about half the length of the metapopulation. The densely connected seagrass meadows of the central GBRWHA are not limited by the supply of propagules; therefore, management should focus on improving environmental conditions that support natural seagrass recruitment and recovery processes. Our study provides a new framework for assessing the impact of global change on the connectivity and persistence of coastal and marine ecosystems. Without this knowledge, management actions, including coastal restoration, may prove unnecessary and be unsuccessful.Alana Grech, Emmanuel Hanert, Len McKenzie, Michael Rasheed, Christopher Thomas, Samantha Tol, Mingzhu Wang, Michelle Waycott, Jolan Wolter, Rob Cole
A comparison of three Eulerian numerical methods for fractional-order transport models
No full textTracer transport in complex systems like turbulent flows or heterogeneous porous media is now more and more regarded as a non-local process that can hardly be represented by second-order diffusion models. In this work, we consider diffusion models that assume that tracer particles follow a heavy-tail L,vy distribution, which allows for large displacements. We show that such an assumption leads to a fractional-order diffusion operator in the governing equation for tracer concentration. A comparison of three Eulerian numerical methods to discretize that equation is then performed. These consist of the finite difference, finite element and spectral element methods. We suggest that non-local methods, like the spectral element method, are better suited to transport models with fractional-order diffusion operators
A fractional diffusion model of CD8+ T cells response to parasitic infection in the brain
No full textToxoplasma gondii (T. gondii) is a parasitic pathogen that causes serious brain diseases in fetuses and patients with immunodeficiency, particularly AIDS patients. In the field of immunology, a large number of studies have shown that effector CD8+ T cells can respond to T. gondii infection in the brain tissue through controlling the proliferation of intracellular parasites and killing infected brain cells. These protective mechanisms do not occur without T cell movement and searching for infected cells, as a fundamental feature of the immune system. Following infection with a pathogen in a tissue, in their search for infected cells, CD8+ T cells can perform different stochastic searches, including Lévy and Brownian random walks. Statistical analysis of CD8+ T cell movement in the brain of T. gondii-infected mouse has determined that the search strategy of CD8+ T cells in response to infected brain cells could be described by a Lévy random walk. In this work, by considering a Lévy distribution for the displacements, we propose a space fractional-order diffusion equation for the T cell density in the infected brain tissue. Furthermore, we derive a mathematical model representing CD8+ T cell response to infected brain cells. By solving the model equations numerically, we perform a comparison between Lévy and Brownian search strategies. we demonstrate that the Lévy search pattern enables CD8+ T cells to spread over the whole brain tissue and hence they can rapidly destroy infected cells distributed throughout the brain tissue. However, with the Brownian motion assumption, CD8+ T cells travel through the brain tissue more slowly, leading to a slower decline of the infected cells faraway from the source of T cells. Our results show that a Lévy search pattern aids CD8+ T cells in accelerating the elimination of infected cells distributed broadly within the brain tissue. We suggest that a Lévy search strategy could be the result of natural evolution, as CD8+ T cells learn to enhance the immune system efficiency against pathogens
Meshfree Approximation for Multi-Asset Options
No full textWe price multi-asset options by solving their price partial differential equations using a meshfree approach with radial basis functions under jump-diffusion and geometric Brownian motion frameworks. In the geo- metric Brownian motion framework, we propose an effective technique that breaks the multi-dimensional problem to multiple 3D problems. We solve the price PDEs or PIDEs with an implicit meshfree scheme using thin-plate radial basis functions. Meshfree approach is very accurate, has high order of convergence and is easily scalable and adaptable to higher dimensions and different payoff profiles. We also obtain closed form approximations for the option Greeks. We test the model on American crack spread options traded on NYMEX
Front Propagation of Exponentially Truncated Fractional-Order Epidemics
No full textThe existence of landscape constraints in the home range of living organisms that adopt Lévy-flight movement patterns, prevents them from making arbitrarily large displacements. Their random movements indeed occur in a finite space with an upper bound. In order to make realistic models, by introducing exponentially truncated Lévy flights, such an upper bound can thus be taken into account in the reaction-diffusion models. In this work, we have investigated the influence of the λ-truncated fractional-order diffusion operator on the spatial propagation of the epidemics caused by infectious diseases, where λ is the truncation parameter. Analytical and numerical simulations show that depending on the value of λ, different asymptotic behaviours of the travelling-wave solutions can be identified. For small values of λ(λ≳0), the tails of the infective waves can decay algebraically leading to an exponential growth of the epidemic speed. In that case, the truncation has no impact on the superdiffusive epidemics. By increasing the value of λ, the algebraic decaying tails can be tamed leading to either an upper bound on the epidemic speed representing the maximum speed value or the generation of the infective waves of a constant shape propagating at a minimum constant speed as observed in the classical models (second-order diffusion epidemic models). Our findings suggest that the truncated fractional-order diffusion equations have the potential to model the epidemics of animals performing Lévy flights, as the animal diseases can spread more smoothly than the exponential acceleration of the human disease epidemics
A radial basis functions method for fractional diffusion equations
No full textOne of the ongoing issues with fractional diffusion models is the design of an efficient high-order numerical discretization. This is one of the reasons why fractional diffusion models are not yet more widely used to describe complex systems. In this paper, we derive a radial basis functions (RBF) discretization of the one-dimensional space-fractional diffusion equation. In order to remove the ill-conditioning that often impairs the convergence rate of standard RBF methods, we use the RBF-QR method. By using this algorithm, we can analytically remove the ill-conditioning that appears when the number of nodes increases or when basis functions are made increasingly flat. The resulting RBF-QR-based method exhibits an exponential rate of convergence for infinitely smooth solutions that is comparable to the one achieved with pseudo-spectral methods. We illustrate the flexibility of the algorithm by comparing the standard RBF and RBF-QR methods for two numerical examples. Our results suggest that the global character of the RBFs makes them well-suited to fractional diffusion equations. They naturally take the global behavior of the solution into account and thus do not result in an extra computational cost when moving from a second-order to a fractional-order diffusion model. As such, they should be considered as one of the methods of choice to discretize fractional diffusion models of complex systems
Multiscale modelling of hydro-biogeochemical fluxes along the Danube delta-Black Sea land-sea continuum
No full textpeer reviewedThe Danube River is the second longest river in Europe. It passes through 10 countries before emptying in the Black Sea. The Danube Delta, largest nearly undisturbed wetland in Europe, plays a buffering role between the river and the sea. Eutrophication in the coastal zone due to the increase of nutrients coming from the river causes important biological and financial losses since the 1970s. However, despite this and the importance of the Danube-Danube Delta-Black Sea system, the hydro and biogeochemical fluxes in this system remain largely understudied. The main objective of this PhD is to model and quantify the interactions between the Danube delta and the Black Sea, from hourly to multi-annual time scales. More specifically, we aim to evaluate how the biogeochemical fluxes of the North-western shelf (NWS) (i.e. limited by the 100m isobath) impact and are impacted by the small-scale variability of the three branches of the Danube Delta (i.e. Chilia, Sulina and Sfântul Gheorghe)
Multi-scale modelling of biogeochemical fluxes along the Danube land-sea continuum
No full textpeer reviewedThe Danube River is the second longest river in Europe. It passes through 10 countries before emptying in the Black Sea. The Danube Delta, largest nearly undisturbed wetland in Europe, plays a buffering role between the river and the sea. Eutrophication in the coastal zone due to the increase of nutrients coming from the river causes important biological and financial losses since the 1970s. However, despite this and the importance of the Danube-Danube Delta-Black Sea system, the hydro and biogeochemical fluxes in this system remain largely understudied. We aim to model and quantify the interactions between the Danube delta and the Black Sea, from hourly to multi-annual time scales, using an unstructured-mesh hydrodynamic model. More specifically, we aim to evaluate how the biogeochemical fluxes of the North-western shelf (NWS) (i.e. limited by the 100m isobath) impact and are impacted by the small-scale variability of the three branches of the Danube Delta (i.e. Chilia, Sulina and Sfântul Gheorghe). We will then assess the potential impact of climate change and socioeconomic development on the transfer of water, salt and biogeochemical elements to the sea by running the model under different IPCC scenarios (SSP1-2.6 and SSP5-8.5). This will allow us to evaluate the mitigation potential of the Danube delta on eutrophication phenomenon in the Black Sea, linked with humans developments and socioeconomics pathways, and give recommendations to lessen its impacts in the North-western shelf region
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