A scaled version of the double-mean-reverting model for VIX derivatives

As the Heston model is not consistent with VIX data in real market well enough, alternative stochastic volatility models including the double-mean-reverting model of Gatheral (in: Bachelier Congress, 2008) have been developed to overcome its limitation. The double-mean-reverting model is a three factor model successfully reflecting the empirical dynamics of the variance but there is no closed form solution for VIX derivatives and SPX options and thus calibration using conventional techniques may be slow. In this paper, we propose a fast mean-reverting version of the double-mean-reverting model. We obtain a closed form approximation for VIX derivatives and show how it is effective by comparing it with the Heston model and the double-mean-reverting model.     

A computational model for interfaces

Decompositions of the plane into disjoint components separated by curves occur frequently. We describe a package of subroutines which provides facilities for defining, building, and modifying such decompositions and for efficiently solving various point and area location problems. Beyond the point that the specification of this package may be useful to others, we reach the broader conclusion that well-designed data structures and support routines allow the use of more conceptual or non-numerical portions of mathematics in the computational process, thereby extending greatly the potential scope of the use of computers in scientific problem solving. Ideas from conceptual mathematics, symbolic computation, and computer science can be utilized within the framework of scientific computing and have an important role to play in that area.     

Large deviations for two scaled diffusions

Summary. We formulate large deviations principle (LDP) for diffusion pair (X ^ɛ ,ξ ^ɛ )=(X _t ^ɛ ,ξ _t ^ɛ ), where first component has a small diffusion parameter while the second is ergodic Markovian process with fast time. More exactly, the LDP is established for (X ^ɛ ,ν ^ɛ ) with ν ^ɛ (dt, dz) being an occupation type measure corresponding to ξ _t ^ɛ . In some sense we obtain a combination of Freidlin–Wentzell’s and Donsker–Varadhan’s results. Our approach relies on the concept of the exponential tightness and Puhalskii’s theorem. Received: 29 June 1995/In revised form: 14 February 1996     

A positive finite-difference model in the computational simulation of complex biological film models

In this work, we design a linear, two-step, finite-difference method to approximate the solutions of a biological system that describes the interaction between a microbial colony and a surrounding substrate. The model is a system of four partial differential equations with nonlinear diffusion and reaction, and the colony is formed by an active portion, an inert component and the contribution of extracellular polymeric substances. In this work, we extend the computational approach proposed by Eberl and Demaret [A finite difference scheme for a degenerated diffusion equation arising in microbial ecology, Electr. J. Differ. Equ. 15 (2007) pp. 77–95], in order to design a numerical technique to approximate the solutions of a more complicated model proposed in the literature. As we will see in this work, this approach guarantees that positive and bounded initial solutions will evolve uniquely into positive and bounded, new approximations. We provide numerical simulations to evince the preservation of the positive character of solutions.     

A micromechanical model for the transformation induced plasticity in polycrystalline steels

Due to the effect of transformation induced plasticity (TRIP) , TRIP-steels are very promising materials, e.g. for the automobile industry. The material behavior is characterized by very complex inner processes, namely phase transformation coupled with plastic deformation and kinematic hardening. We establish a micromechanical model which uses the volume fractions of the single phases, the plastic strain and the hardening parameter in every grain of the polycrystalline material as internal variables. Furthermore, we apply the Principle of the Minimum of the Dissipation Potential to derive the associated evolution equations. The use of a coupled dissipation functional and a combined Voigt/Reuss bound directly results in coupled evolution equations for the internal variables and in one combined yield function. Additionally, we show numerical results which prove our model's ability to give a first prediction of the TRIP-steels' complex material behavior. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A computational model for solid waste management with application

A model for regional solid waste management as a network flow problem is described, and a special purpose algorithm is developed. The model is applied to waste management and facility siting decisions in the Munich Metropolitan Area in the Federal Republic of Germany.     

A computational model for human eye-movements in military simulations

Models of eye movements of an observer searching for human targets are helpful in developing accurate models of target acquisition times and false positive detections. We develop a new model describing the distribution of gaze positions for an observer which includes both bottom-up (salience) and top-down (task dependent) factors. We validate the combined model against a bottom-up model from the literature and against the bottom up and top down parts alone using human performance data on stationary targets. The new model is shown to be significantly better. The new model requires a large amount of data about the terrain and the target that is obtained directly from the 3D simulation through an automated process.     

A simulation model for emergency evacuation

This paper describes the development of a prototype spatial decision support system for use by emergency planners in developing contingency plans for evacuations from disaster areas. It links together a geographical information system (ARC/INFO) with a specially written object-oriented micro-simulator via a windowing computer operating system. The details of the system are described, its limitations are discussed and potential enhancements are identified.     

A convection model for fire spread simulation

We present a convection model which can be coupled with fire propagation models in order to take into account the wind and the slope which are two of the most relevant factors affecting surface fire spread. An asymptotic analysis gives a three-dimensional convective model governed by a two-dimensional equation.     

A simple computational model of digestion in the marine mussel

A simplified model of a marine mussel is proposed. We model the digestive system as a cellular analogue, physically partitioned into a lysosome and endosome, with the flow of particulate carbon to represent energy. The parameters in the rate equations that govern the interactions between compartments are assumed to be a simple linear form but are consistent with experiment and observation. The model is tested first by using continuous feeding and then by using a periodic feeding representative of tidal input. The responses in both cases produce interesting results compatible with observations of the biology of the animal. We define a “health function” which indicates whether or not the animal survives. It is found that survival is critically dependent on lysosomal efficiency.     

A simulation model for American football plays

A Monte Carlo model is presented which simulates the time history of the players' positions and velocities. Passing plays are excluded. The play is broken into constant-interval epochs at which the players select their respective strategies. These in turn are used in conjuctions with kinematic equations to update the players' state variables. Various objectives are formulated via nonlinear programming problems for the three classes of players (offensive ball-carrier, defensive tacklers and offensive blockers). Interactions between players (blocking and tackling) are postulated from considerations of particle dynamics. Sample results are presented and methods of validating the model are discussed.     

A computational framework for spatially explicit agroecosystem modeling: Application to regional simulation

Site-based agroecosystem model has been applied at regional and state level to enable comprehensive analyses of environmental sustainability of food and biofuel production. However, spatially explicit ecosystem simulations over large landscape present computational challenges. This paper presents a framework to support spatially explicit agroecosystem modeling and data analysis over large landscape, which includes four major phases of agroecosystem simulation: simulation data preparation, site-based simulation on high performance computers, data management and data analysis. Then, a case study on a regional intensive modeling area (RIMA) was presented as an application to demonstrate the system implementation and capability.     

A computational model for multi-agent E-commerce negotiations with adaptive negotiation behaviors

This paper presents a computational model to organize multi-agent E-commerce negotiations with adaptive negotiation behaviors aiming at enhancing the negotiation flexibilities of software agents. Firstly, the computational E-commerce negotiation model covering negotiation protocol, negotiation issues and negotiation strategies is specified to assist agents’ computing functions. Then, a three-staged adaptive negotiation behavior configuration mechanism is proposed to tackle the negotiation dynamics. In the pre-negotiation stage, agents’ negotiation behaviors are deployed by the case-based strategy assignment mechanism; in the on-going negotiation stage, opponents’ negotiation behaviors are tracked through the neural network learning model; in the post-negotiation stage, opponents’ concession functions are recorded using the time series measure. Finally, the computational negotiation model is tested through hypothetical negotiation cases. The outcomes show that the adaptive negotiation behavior configuration mechanism can benefit an agent to win more in the E-commerce negotiation.     

A computational toy model for shallow landslides: Molecular dynamics approach

The aim of this paper is to propose a 2D computational algorithm for modeling the triggering and propagation of shallow landslides caused by rainfall. We used a molecular dynamics (MD) approach, similar to the discrete element method (DEM), that is suitable to model granular material and to observe the trajectory of a single particle, so to possibly identify its dynamical properties. We consider that the triggering of shallow landslides is caused by the decrease of the static friction along the sliding surface due to water infiltration by rainfall. Thence the triggering is caused by the two following conditions: (a) a threshold speed of the particles and (b) a condition on the static friction, between the particles and the slope surface, based on the Mohr–Coulomb failure criterion. The latter static condition is used in the geotechnical model to estimate the possibility of landslide triggering. The interaction force between particles is modeled, in the absence of experimental data, by means of a potential similar to the Lennard-Jones one. The viscosity is also introduced in the model and for a large range of values of the model’s parameters, we observe a characteristic velocity pattern, with acceleration increments, typical of real landslides. The results of simulations are quite promising: the energy and time triggering distribution of local avalanches show a power law distribution, analogous to the observed Gutenberg–Richter and Omori power law distributions for earthquakes. Finally, it is possible to apply the method of the inverse surface displacement velocity [4] for predicting the failure time.     

A stochastic model for two interacting species

An exactly solvable stochastic model for two interacting species with a prey-predator relationship in the presence of self-interaction is investigated. The parameters describing the interactions are assumed to be represented by a dichotomic Markov process. Explicit expressions are derived for the time development of the average of the logarithm of the population size in respect of each species and their asymptotic behaviours are discussed.     

A class of scaled direct methods for linear systems

A generalization of the class of direct methods for linear systems recently introduced by Abaffy, Broyden and Spedicato is obtained by applying these algorithms to a scaled system. The resulting class contains an essentially free parameter at each step, giving a unified approach to finitely terminating methods for linear systems. Various properties of the generalized class are presented. Particular attention is paid to the subclasses that contain the classic Hestenes-Stiefel method and the Hegedus-Bodocs biorthogonalization methods.This work was partially supported by CNR under contract 85.02648.01.     

A monte carlo model for simulation of tank battles

A Monte Carlo model for simulation of company-level tank battles is described. The simulation is started with an observation phase. The probability of discovery is dependent upon properties of the terrain etc. Target selection is simulated deterministically with priority rules. Every unit belongs to one of the following states of fight: undamaged, able to shoot only, able to move only, shocked and out of action.It is possible to simulate surprise attacks and battles after a sudden contact if the units are assumed to fight from the same position during the whole battle. In a later version of the model, the units are permitted to show as much of themselves as they wish during the battle. Thus it is possible to simulate (small) changes of position, initiated by the current events.     

A mathematical programming computational model for disproportionate collapse analysis of steel building frames

Disproportionate collapse analysis aims to assure that frames, a common structural system of buildings, can survive unforeseen local events and a central modeling tool of such abnormal deterioration is the concept of column loss. This paper formulates an appropriate computational model on the basis of mathematical optimization, using the collapse load analysis problem of steel frames with pre-existing damage. A respective collapse load robustness measure is proposed. The model has the ability to consider both full and partial column/node removals. It renders to be a linear programming model, if the US steel design regulations are used. A practical example is presented and several aspects are discussed.