scholarly journals A Stochastic Harmonic Oscillator Temperature Model for the Valuation of Weather Derivatives

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2890
Author(s):  
Alessio Giorgini ◽  
Rogemar S. Mamon ◽  
Marianito R. Rodrigo
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Harmonic Oscillator ◽  
Numerical Simulations ◽  
Model Parameters ◽  
Call Option ◽  
Temperature Model ◽  
Option Prices ◽  
Harmonic Oscillator Model ◽  
Temperature Dynamics

Stochastic processes are employed in this paper to capture the evolution of daily mean temperatures, with the goal of pricing temperature-based weather options. A stochastic harmonic oscillator model is proposed for the temperature dynamics and results of numerical simulations and parameter estimation are presented. The temperature model is used to price a one-month call option and a sensitivity analysis is undertaken to examine how call option prices are affected when the model parameters are varied.

scholarly journals Approximate ordinary differential equations for the optimal exercise boundaries of American put and call options

2013 ◽  
Vol 25 (1) ◽  
pp. 27-43 ◽  
Author(s):  
MARIANITO R. RODRIGO
Keyword(s):  
Differential Equations ◽  
Fluid Mechanics ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Boundary Layers ◽  
Mellin Transform ◽  
Call Option ◽  
Option Prices ◽  
Analytical Formulas ◽  
American Put

We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mellin transform and an adaptation of the Kármán–Pohlausen technique for boundary layers in fluid mechanics.

Li-Ion Cell Aging Model Online Parameter Estimation for Improved Prognosis

2016 ◽  
Author(s):  
Punit Tulpule ◽  
Chin-Yao Chang ◽  
Giorgio Rizzoni
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Lithium Ion ◽  
Remaining Useful Life ◽  
Estimation Methods ◽  
Cell Aging ◽  
Model Parameters ◽  
Positive Electrodes ◽  
Aging Model ◽  
Estimation Algorithms

In this paper, a semi-empirical aging model of lithium-ion pouch cells containing blended spinel and layered-oxide positive electrodes is calibrated using aging campaigns. Sensitivity analysis is done on this model to identify the effect of parameter variations on the State of Health (SOH) prediction. The sensitivity analysis shows that the aging model alone is not robust enough to perform long term predictions, hence we propose to use online parameter estimation algorithms to adapt the model parameters. Four different estimation methods are compared using aging campaign. It is demonstrated that the estimation algorithms improve aging model leading to significant improvement in Remaining Useful Life (RUL) prediction.

Systematic Parameter Estimation and Sensitivity Analysis Using a Multidimensional PEMFC Model Coupled With DAKOTA

2010 ◽  
Author(s):  
Brian Carnes ◽  
Ken S. Chen ◽  
Fangming Jiang ◽  
Gang Luo ◽  
Chao-Yang Wang
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Proton Exchange Membrane ◽  
Computational Models ◽  
Proton Exchange ◽  
Operating Conditions ◽  
Critical Parameters ◽  
Model Parameters ◽  
Two Phase ◽  
Manual Adjustment

Current computational models for proton exchange membrane fuel cells (PEMFCs) include a large number of parameters such as boundary conditions, material properties, and numerous parameters used in sub-models for membrane transport, two-phase flow and electrochemistry. In order to successfully use a computational PEMFC model in design and optimization, it is important to identify critical parameters under a wide variety of operating conditions, such as relative humidity, current load, temperature, etc. Moreover, when experimental data is available in the form of polarization curves or local distribution of current and reactant/product species (e.g., O2, H2O concentrations), critical parameters can be estimated in order to enable the model to better fit the data. Sensitivity analysis and parameter estimation are typically performed using manual adjustment of parameters, which is also common in parameter studies. We present work to demonstrate a systematic approach based on using a widely available toolkit developed at Sandia called DAKOTA that supports many kinds of design studies, such as sensitivity analysis as well as optimization and uncertainty quantification. In the present work, we couple a multidimensional PEMFC model (which is being developed, tested and later validated in a joint effort by a team from Penn State Univ. and Sandia National Laboratories) with DAKOTA through the mapping of model parameters to system responses. Using this interface, we demonstrate the efficiency of performing simple parameter studies as well as identifying critical parameters using sensitivity analysis. Finally, we show examples of optimization and parameter estimation using the automated capability in DAKOTA.

scholarly journals Sensitivity analysis and parameter estimation for the distributed modeling of infiltration excess overland flow

2007 ◽  
Vol 4 (1) ◽  
pp. 363-405 ◽  
Author(s):  
W. Castaings ◽  
D. Dartus ◽  
F.-X. Le Dimet ◽  
G.-M. Saulnier
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Overland Flow ◽  
Flash Flood ◽  
Parametric Uncertainty ◽  
Optimization Techniques ◽  
Model Parameters ◽  
Adjoint Sensitivity ◽  
Gradient Based ◽  
Infiltration Excess

Abstract. The variational methods widely used for other environmental systems are applied to a spatially distributed flash flood model coupling kinematic wave overland flow and Green Ampt infiltration. Using an idealized configuration where only parametric uncertainty is addressed, the potential of this approach is illustrated for sensitivity analysis and parameter estimation. Adjoint sensitivity analysis provides an extensive insight into the relation between model parameters and the hydrological response and enables the use of efficient gradient based optimization techniques.

The Usefulness of Spectroscopic Simulations

2020 ◽  
Vol 74 (3) ◽  
pp. 305-313
Author(s):  
Milan Milosevic ◽  
Nils Wendland ◽  
Robert E. Lee ◽  
Brian W. Gregory
Keyword(s):  
Harmonic Oscillator ◽  
Infrared Spectra ◽  
Optical Constants ◽  
Experimental Spectrum ◽  
Molecular Polarizability ◽  
Model Parameters ◽  
Calculated Spectrum ◽  
Harmonic Oscillator Model ◽  
Spectral Simulations ◽  
Close Fit

This article presents a method for extracting the optical constants of homogeneous isotropic materials using the infrared spectra of that material. The method is based on using the harmonic oscillator model of molecular polarizability to obtain optical constants, then calculating the spectrum, comparing the calculated spectrum to an experimental spectrum of the material, and adjusting the model parameters until a close fit between the spectra is obtained. Corrections that need to be made to the experimental spectra in order to remove instrumental distortions are also briefly described. The remainder of the article centers on describing how the optical constants can be used to simulate spectra of that material in different experimental arrangements and the benefits that spectral simulations afford to experimentalists.

Parameter Estimation and Sensitivity Analysis of a Nonlinearly Elastic Static Lung Model

1985 ◽  
Vol 107 (4) ◽  
pp. 315-320 ◽  
Author(s):  
J. R. Ligas ◽  
G. M. Saidel ◽  
F. P. Primiano
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Least Squares ◽  
Static Pressure ◽  
Optimal Parameter ◽  
Elastic Strain Energy ◽  
Lung Model ◽  
Model Parameters ◽  
Least Squares Fit ◽  
Parameter Values

A model for the static pressure-volume behavior of the lung parenchyma based on a pseudo-elastic strain energy function was tested. Values of the model parameters and their variances were estimated by an optimal least-squares fit of the model-predicted pressures to the corresponding data from excised, saline-filled dog lungs. Although the model fit data from twelve lungs very well, the coefficients of variation for parameter values differed greatly. To analyze the sensitivity of the model output to its parameters, we examined an approximate Hessian, H, of the least-squares objective function. Based on the determinant and condition number of H, we were able to set formal criteria for choosing the most reliable estimates of parameter values and their variances. This in turn allowed us to specify a normal range of parameter values for these dog lungs. Thus the model not only describes static pressure-volume data, but also uses the data to estimate parameters from a fundamental constitutive equation. The optimal parameter estimation and sensitivity analysis developed here can be widely applied to other physiologic systems.

scholarly journals Dynamics of Toxoplasmosis Disease in Cats population with vaccination

2021 ◽  
pp. 17-25
Author(s):  
Idris Babaji Muhammad ◽  
Salisu Usaini
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Simulations ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Vaccination Rate ◽  
Steady States ◽  
Model Parameters ◽  
Threshold Parameter ◽  
Globally Stable ◽  
Disease Free

We extend the deterministic model for the dynamics of toxoplasmosis proposed by Arenas et al. in 2010, by separating vaccinated and recovered classes. The model exhibits two equilibrium points, the disease-free and endemic steady states. These points are both locally and globally stable asymptotically when the threshold parameter Rv is less than and greater than unity, respectively. The sensitivity analysis of the model parameters reveals that the vaccination parameter $\pi$ is more sensitive to changes than any other parameter. Indeed, as expected the numerical simulations reveal that the higher the vaccination rate of susceptible individuals the smaller the value of the threshold Rv (i.e., increase in $\pi$ results in the decrease in Rv , leading to the eradication of toxoplasmosis in cats population.

scholarly journals Constrained Parameter Estimation for a Mechanistic Kinetic Model of Cobalt–Hydrogen Electrochemical Competition during a Cobalt Removal Process

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 387
Author(s):  
Yiting Liang ◽  
Yuanhua Zhang ◽  
Yonggang Li
Keyword(s):  
Parameter Estimation ◽  
Kinetic Model ◽  
Model Parameters ◽  
Hydrogen Ions ◽  
Removal Process ◽  
Cobalt Removal ◽  
Estimation Scheme ◽  
Zinc Hydrometallurgy ◽  
The Impact ◽  
Parameter Estimation Scheme

A mechanistic kinetic model of cobalt–hydrogen electrochemical competition for the cobalt removal process in zinc hydrometallurgical was proposed. In addition, to overcome the parameter estimation difficulties arising from the model nonlinearities and the lack of information on the possible value ranges of parameters to be estimated, a constrained guided parameter estimation scheme was derived based on model equations and experimental data. The proposed model and the parameter estimation scheme have two advantages: (i) The model reflected for the first time the mechanism of the electrochemical competition between cobalt and hydrogen ions in the process of cobalt removal in zinc hydrometallurgy; (ii) The proposed constrained parameter estimation scheme did not depend on the information of the possible value ranges of parameters to be estimated; (iii) the constraint conditions provided in that scheme directly linked the experimental phenomenon metrics to the model parameters thereby providing deeper insights into the model parameters for model users. Numerical experiments showed that the proposed constrained parameter estimation algorithm significantly improved the estimation efficiency. Meanwhile, the proposed cobalt–hydrogen electrochemical competition model allowed for accurate simulation of the impact of hydrogen ions on cobalt removal rate as well as simulation of the trend of hydrogen ion concentration, which would be helpful for the actual cobalt removal process in zinc hydrometallurgy.

scholarly journals A Sensitivity Analysis of the SPACSYS Model

Agriculture ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 624
Author(s):  
Yan Shan ◽  
Mingbin Huang ◽  
Paul Harris ◽  
Lianhai Wu
Keyword(s):  
Sensitivity Analysis ◽  
Wheat Yield ◽  
Climatic Conditions ◽  
Water Dynamics ◽  
Ecological Modelling ◽  
Soil Conditions ◽  
Model Parameters ◽  
Nutrient Inputs ◽  
Nutrient Pool ◽  
Wheat Field

A sensitivity analysis is critical for determining the relative importance of model parameters to their influence on the simulated outputs from a process-based model. In this study, a sensitivity analysis for the SPACSYS model, first published in Ecological Modelling (Wu, et al., 2007), was conducted with respect to changes in 61 input parameters and their influence on 27 output variables. Parameter sensitivity was conducted in a ‘one at a time’ manner and objectively assessed through a single statistical diagnostic (normalized root mean square deviation) which ranked parameters according to their influence of each output variable in turn. A winter wheat field experiment provided the case study data. Two sets of weather elements to represent different climatic conditions and four different soil types were specified, where results indicated little influence on these specifications for the identification of the most sensitive parameters. Soil conditions and management were found to affect the ranking of parameter sensitivities more strongly than weather conditions for the selected outputs. Parameters related to drainage were strongly influential for simulations of soil water dynamics, yield and biomass of wheat, runoff, and leaching from soil during individual and consecutive growing years. Wheat yield and biomass simulations were sensitive to the ‘ammonium immobilised fraction’ parameter that related to soil mineralization and immobilisation. Simulations of CO2 release from the soil and soil nutrient pool changes were most sensitive to external nutrient inputs and the process of denitrification, mineralization, and decomposition. This study provides important evidence of which SPACSYS parameters require the most care in their specification. Moving forward, this evidence can help direct efficient sampling and lab analyses for increased accuracy of such parameters. Results provide a useful reference for model users on which parameters are most influential for different simulation goals, which in turn provides better informed decision making for farmers and government policy alike.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

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