Co-evolution of Content Popularity and Delivery in Mobile P2P Networks

Mobile P2P technology provides a scalable approach to content delivery to a large number of users on their mobile devices. In this work, we study the dissemination of a \emph{single} content (e.g., an item of news, a song or a video clip) among a population of mobile nodes. Each node in the population is either a \emph{destination} (interested in the content) or a potential \emph{relay} (not yet interested in the content). There is an interest evolution process by which nodes not yet interested in the content (i.e., relays) can become interested (i.e., become destinations) on learning about the popularity of the content (i.e., the number of already interested nodes). In our work, the interest in the content evolves under the \emph{linear threshold model}. The content is copied between nodes when they make random contact. For this we employ a controlled epidemic spread model. We model the joint evolution of the copying process and the interest evolution process, and derive the joint fluid limit ordinary differential equations. We then study the selection of the parameters under the content provider's control, for the optimization of various objective functions that aim at maximizing content popularity and efficient content delivery.Comment: 21 pages, 16 figure

Analytic Approximations for Spread Options

This paper expresses the price of a spread option as the sum of the prices of two compound options. One compound option is to exchange vanilla call options on the two underlying assets and the other is to exchange the corresponding put options. This way we derive a new analytic approximation for the price of a European spread option, and a corresponding approximation for each of its price, volatilty and correlation hedge ratios. Our approach has many advantages over existing analytic approximations, which have limited validity and an indeterminacy that renders them of little practical use. The compound exchange option approximation for European spread options is then extended to American spread options on assets that pay dividends or incur carry costs. Simulations quantify the accuracy of our approach; we also present an empirical application, to the American crack spread options that are traded on NYMEX. For illustration, we compare our results with those obtained using the approximation attributed to Kirk (1996) which is commonly used by traders.Spread options, exchange options, American options, analytic formula, Kirks approximation, correlation skew

Meshfree Approximation for Multi-Asset Options

We 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

Analytic Approximations for Multi-Asset Option Pricing

We derive a general analytic approximation for pricing basket options on N assets, which is extended to analytic approximations for pricing general rainbow options, including best-of and worst-of N asset options. The key idea is to express the option's price as a sum of prices of various compound exchange options, each with different pairs of sub-ordinate multi- or single-asset options. For some multi-asset options a strong condition holds, whereby each compound exchange option is equivalent to a standard single-asset option under a modified measure, and in such cases an almost exact analytic price exists for the multi-asset option. The underlying asset prices are assumed to follow log-normal processes, although the strong condition can be extended to certain other price processes for the underlying. More generally, approximate analytic prices for multi-asset options are derived using a weak log-normality condition, where the approximation stems from making constant volatility assumptions on the price processes that drive the prices of the sub-ordinate basket options. The analytic formulae for multi-asset option prices, and their Greeks, are defined in a recursive framework. For instance, the option delta is defined in terms of the delta relative to sub-ordinate multi-asset options, and the deltas of these sub-ordinate options with respect to the underlying assets. An empirical study of a particular 4-asset basket option tests the accuracy of our approximation, given some assumed values for the calibrated parameters. Then we demonstrate how to calibrate the model's parameters to market data so that the prices are consistent with the implied volatility and correlation skews of the assets.Basket options, Rainbow options, Best-of and Worst-of options, Compound Exchange Options, Analytic Approximation

Analytic Approximations for Spread Options

Even in the simple case that two price processes follow correlated geometric Brownian motions with constant volatility no analytic formula for the price of a standard European spread option has been derived, except when the strike is zero in which case the option becomes an exchange option. This paper expresses the price of a spread option as the price of a compound exchange option and hence derives a new analytic approximation for its price and hedge ratios. This approximation has several advantages over existing analytic approximations, which have limited validity and an indeterminacy that renders them of little practical use. Simulations quantify the accuracy of our approach and demonstrate the indeterminacy and inaccuracy of other analytic approximations. The American spread option price is identical to the European option price when the two price processes have identical drifts, and otherwise we derive an expression for the early exercise premium. A practical illustration of the model calibration uses market data on American crack spread options.Asset pricing, Spread options, Exchange options, American Options

Modeling and Analysis of Scholar Mobility on Scientific Landscape

Scientific literature till date can be thought of as a partially revealed landscape, where scholars continue to unveil hidden knowledge by exploring novel research topics. How do scholars explore the scientific landscape , i.e., choose research topics to work on? We propose an agent-based model of topic mobility behavior where scholars migrate across research topics on the space of science following different strategies, seeking different utilities. We use this model to study whether strategies widely used in current scientific community can provide a balance between individual scientific success and the efficiency and diversity of the whole academic society. Through extensive simulations, we provide insights into the roles of different strategies, such as choosing topics according to research potential or the popularity. Our model provides a conceptual framework and a computational approach to analyze scholars' behavior and its impact on scientific production. We also discuss how such an agent-based modeling approach can be integrated with big real-world scholarly data.Comment: To appear in BigScholar, WWW 201

Hybrid finite-volume/transported PDF method for the simulation of turbulent reactive flows

A novel computational scheme is formulated for simulating turbulent reactive flows in complex geometries with detailed chemical kinetics. A Probability Density Function (PDF) based method that handles the scalar transport equation is coupled with an existing Finite Volume (FV) Reynolds-Averaged Navier-Stokes (RANS) flow solver. The PDF formulation leads to closed chemical source terms and facilitates the use of detailed chemical mechanisms without approximations. The particle-based PDF scheme is modified to handle complex geometries and grid structures. Grid-independent particle evolution schemes that scale linearly with the problem size are implemented in the Monte-Carlo PDF solver. A novel algorithm, in situ adaptive tabulation (ISAT) is employed to ensure tractability of complex chemistry involving a multitude of species. Several non-reacting test cases are performed to ascertain the efficiency and accuracy of the method. Simulation results from a turbulent jet-diffusion flame case are compared against experimental data. The effect of micromixing model, turbulence model and reaction scheme on flame predictions are discussed extensively. Finally, the method is used to analyze the Dow Chlorination Reactor. Detailed kinetics involving 37 species and 158 reactions as well as a reduced form with 16 species and 21 reactions are used. The effect of inlet configuration on reactor behavior and product distribution is analyzed. Plant-scale reactors exhibit quenching phenomena that cannot be reproduced by conventional simulation methods. The FV-PDF method predicts quenching accurately and provides insight into the dynamics of the reactor near extinction. The accuracy of the fractional time-stepping technique in discussed in the context of apparent multiple-steady states observed in a non-premixed feed configuration of the chlorination reactor