The Experts below are selected from a list of 84198 Experts worldwide ranked by ideXlab platform
Marc Yor - One of the best experts on this subject based on the ideXlab platform.
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a simple stochastic rate model for rate equity hybrid products
Applied Mathematical Finance, 2013Co-Authors: Ernst Eberlein, Dilip B Madan, Martijn Pistorius, Marc YorAbstract:AbstractA positive spot rate model driven by a Gamma Process and correlated with equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r, its integral y and the logarithm of the stock price s under the T-forward measure. The law of the triple is expressed as a nonlinear transform of three independent Processes, a Gamma Process, a variance Gamma Process and a Wiener integral with respect to the Dirichlet Process. The generalized Stieltjes transform of the Wiener integral with respect to the Dirichlet Process is derived in closed form. Inversion of this transform using Schwarz (2005, The generalized Stieltjes transform and its inverse, Journal of Mathematical Physics, 46(1), doi: 10.1063/1.1825077) makes large step simulations possible. Valuing functions are built and hedged using quantization and high dimensional interpolation methods. The hedging objective is taken to be capital minimization as described by Carr, Madan and Vicente Alvarez (2011, Markets, p...
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a simple stochastic rate model for rate equity hybrid products
Social Science Research Network, 2013Co-Authors: Ernst Eberlein, Dilip B Madan, Martijn Pistorius, Marc YorAbstract:A positive spot rate model driven by a Gamma Process and correlated to equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r, its integral y and the logarithm of the stock price s under the T-forward measure. The law of the triple (r,y,s) is expressed as a nonlinear transform of three independent Processes, a Gamma Process, a variance Gamma Process and a Wiener integral with respect to the Dirichlet Process. The generalized Stieltjes transform of the Wiener integral with respect to the Dirichlet Process is derived in closed form. Inversion of this transform using Schwarz (2005, The generalized Stieltjes transform and its inverse, Journal of Mathematical Physics, doi: 10.1063/1.1825077) makes large step simulations possible. Valuing functions are built and hedged using quantization and high dimensional interpolation methods. The hedging objective is taken to be capital minimization as described in Carr, Madan and Vicente Alvarez (2011, Markets, profits, capital, leverage and returns, Journal of Risk, 14, pp. 95-122).
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an infinite dimensional analogue of the lebesgue measure and distinguished properties of the Gamma Process
Journal of Functional Analysis, 2001Co-Authors: N V Tsilevich, A M Vershik, Marc YorAbstract:Abstract We define a one-parameter family L θ of sigma-finite (finite on compact sets) measures in the space of distributions. These measures are equivalent to the laws of the classical Gamma Processes and invariant under an infinite-dimensional abelian group of certain positive multiplicators. This family of measures was first discovered by Gelfand–Graev–Vershik in the context of the representation theory of current groups; here we describe it in direct terms using some remarkable properties of the Gamma Processes. We show that the class of multiplicative measures coincides with the class of zero-stable measures which is introduced in the paper. We give also a new construction of the canonical representation of the current group SL(2, R )X.
Zeyu Wu - One of the best experts on this subject based on the ideXlab platform.
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Lumen Degradation Lifetime Prediction for High-Power White LEDs Based on the Gamma Process Model
IEEE Photonics Journal, 2019Co-Authors: Mesfin Seid Ibrahim, Winco K.c. Yung, Zeyu WuAbstract:Nowadays, due to the advancement of design and manufacturing technology, there are many consumer products with high reliability. Similarly, the competition in the business sector influences the product development time to become shorter and that makes it difficult for manufacturers to evaluate the reliability of current products before new products are released to the market. This phenomenon is manifested in the lighting industry, especially for the high power white light-emitting diodes (LEDs) as these products have a long lifetime and high reliability. Currently, the standard to predict the lifetime of LEDs is based on a deterministic nonlinear least squares method which has low prediction accuracy. To overcome this, degradation models are being used to study the reliability of such products, considering the uncertainties and the quality characteristics whose degradation over a period of time can be related to the product lifetime. A stochastic approach based on Gamma distributed degradation (GDD) is proposed in this study to estimate the long-term lumen degradation lifetime of phosphor-converted white LEDs. An accelerated thermal degradation test was designed to gather luminous flux degradation data which was analyzed based on maximum likelihood estimation (MLE) and the method of moments (MM) to estimate the parameters for the GDD model. The MLE method has shown superiority over MM in terms of the estimation of the model parameters due to its iterative algorithm being likely to find the optimal estimation. The lifetime prediction results show that the accuracy of the proposed method is much better than the TM-21 nonlinear least squares (NLS) approach which makes it promising for future industrial applications.
Narayanaswamy Balakrishnan - One of the best experts on this subject based on the ideXlab platform.
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Accelerated Degradation Analysis for the Quality of a System Based on the Gamma Process
IEEE Transactions on Reliability, 2015Co-Authors: Man Ho Ling, Kwok Leung Tsui, Narayanaswamy BalakrishnanAbstract:As most systems these days are highly reliable with long lifetimes, failures of systems become rare; consequently, traditional failure time analysis may not be able to provide a precise assessment of the system reliability. In this regard, a degradation measure, as a percentage of the initial value, is an alternate way of describing the system health. This paper presents accelerated degradation analysis that characterizes the health and quality of systems with monotonic and bounded degradation. The maximum likelihood estimates (MLEs) of the model parameters are derived, based on a Gamma Process, time-scale transformation, and a power link function for associating the covariates. Then, methods of estimating the reliability, the mean and median lifetime, the conditional reliability, and the remaining useful life of systems under normal use conditions are all described. Moreover, approximate confidence intervals for the parameters of interest are developed based on the observed Fisher information matrix. A model validation metric with exact power is introduced. A Monte Carlo simulation study is carried out for evaluating the performance of the proposed methods. For an illustration of the proposed model, and the methods of inference developed here, a numerical example involving light intensity of light emitting diodes (LED) is analyzed.
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Optimal Burn-In Policy for Highly Reliable Products Using Gamma Degradation Process
IEEE Transactions on Reliability, 2011Co-Authors: Chih-chun Tsai, Sheng-tsaing Tseng, Narayanaswamy BalakrishnanAbstract:Burn-in test is a manufacturing Process applied to products to eliminate latent failures or weak components in the factory before the products reach customers. The traditional burn-in test over a short period of time to collect time-to-failure or go/no-go data is rather inefficient. This decision problem can be solved if there exists a suitable quality characteristic (QC) whose degradation over time can be related to the lifetime of the product. Recently, optimal burn-in policies have been discussed in the literature assuming that the underlying degradation path follows a Wiener Process. However, the degradation model of many materials (especially in the case of fatigue data) may be more appropriately modeled by a Gamma Process that exhibits a monotone-increasing pattern. Here, motivated by laser data, we first -propose a mixed Gamma Process to describe the degradation path of the product. Next, we present a decision rule for classifying a unit as typical or weak. A cost model is used to determine the optimal termination time of a burn-in test, and a motivating example is then presented to illustrate the proposed procedure. Finally, a simulation study is carried out to examine the effect of wrongly treating a mixed Gamma Process as a mixed Wiener Process, and the obtained results reveal that the effect on the probabilities of misclassification is not negligible.
Ernst Eberlein - One of the best experts on this subject based on the ideXlab platform.
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a simple stochastic rate model for rate equity hybrid products
Applied Mathematical Finance, 2013Co-Authors: Ernst Eberlein, Dilip B Madan, Martijn Pistorius, Marc YorAbstract:AbstractA positive spot rate model driven by a Gamma Process and correlated with equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r, its integral y and the logarithm of the stock price s under the T-forward measure. The law of the triple is expressed as a nonlinear transform of three independent Processes, a Gamma Process, a variance Gamma Process and a Wiener integral with respect to the Dirichlet Process. The generalized Stieltjes transform of the Wiener integral with respect to the Dirichlet Process is derived in closed form. Inversion of this transform using Schwarz (2005, The generalized Stieltjes transform and its inverse, Journal of Mathematical Physics, 46(1), doi: 10.1063/1.1825077) makes large step simulations possible. Valuing functions are built and hedged using quantization and high dimensional interpolation methods. The hedging objective is taken to be capital minimization as described by Carr, Madan and Vicente Alvarez (2011, Markets, p...
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a simple stochastic rate model for rate equity hybrid products
Social Science Research Network, 2013Co-Authors: Ernst Eberlein, Dilip B Madan, Martijn Pistorius, Marc YorAbstract:A positive spot rate model driven by a Gamma Process and correlated to equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r, its integral y and the logarithm of the stock price s under the T-forward measure. The law of the triple (r,y,s) is expressed as a nonlinear transform of three independent Processes, a Gamma Process, a variance Gamma Process and a Wiener integral with respect to the Dirichlet Process. The generalized Stieltjes transform of the Wiener integral with respect to the Dirichlet Process is derived in closed form. Inversion of this transform using Schwarz (2005, The generalized Stieltjes transform and its inverse, Journal of Mathematical Physics, doi: 10.1063/1.1825077) makes large step simulations possible. Valuing functions are built and hedged using quantization and high dimensional interpolation methods. The hedging objective is taken to be capital minimization as described in Carr, Madan and Vicente Alvarez (2011, Markets, profits, capital, leverage and returns, Journal of Risk, 14, pp. 95-122).
Dilip B Madan - One of the best experts on this subject based on the ideXlab platform.
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self decomposability of weak variance generalised Gamma convolutions
Stochastic Processes and their Applications, 2020Co-Authors: Boris Buchmann, Dilip B MadanAbstract:Abstract Weak variance generalised Gamma convolution Processes are multivariate Brownian motions weakly subordinated by multivariate Thorin subordinators. Within this class, we extend a result from strong to weak subordination that a driftless Brownian motion gives rise to a self-decomposable Process. Under moment conditions on the underlying Thorin measure, we show that this condition is also necessary. We apply our results to some prominent Processes such as the weak variance alpha–Gamma Process, and illustrate the necessity of our moment conditions in some cases.
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a simple stochastic rate model for rate equity hybrid products
Applied Mathematical Finance, 2013Co-Authors: Ernst Eberlein, Dilip B Madan, Martijn Pistorius, Marc YorAbstract:AbstractA positive spot rate model driven by a Gamma Process and correlated with equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r, its integral y and the logarithm of the stock price s under the T-forward measure. The law of the triple is expressed as a nonlinear transform of three independent Processes, a Gamma Process, a variance Gamma Process and a Wiener integral with respect to the Dirichlet Process. The generalized Stieltjes transform of the Wiener integral with respect to the Dirichlet Process is derived in closed form. Inversion of this transform using Schwarz (2005, The generalized Stieltjes transform and its inverse, Journal of Mathematical Physics, 46(1), doi: 10.1063/1.1825077) makes large step simulations possible. Valuing functions are built and hedged using quantization and high dimensional interpolation methods. The hedging objective is taken to be capital minimization as described by Carr, Madan and Vicente Alvarez (2011, Markets, p...
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a simple stochastic rate model for rate equity hybrid products
Social Science Research Network, 2013Co-Authors: Ernst Eberlein, Dilip B Madan, Martijn Pistorius, Marc YorAbstract:A positive spot rate model driven by a Gamma Process and correlated to equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r, its integral y and the logarithm of the stock price s under the T-forward measure. The law of the triple (r,y,s) is expressed as a nonlinear transform of three independent Processes, a Gamma Process, a variance Gamma Process and a Wiener integral with respect to the Dirichlet Process. The generalized Stieltjes transform of the Wiener integral with respect to the Dirichlet Process is derived in closed form. Inversion of this transform using Schwarz (2005, The generalized Stieltjes transform and its inverse, Journal of Mathematical Physics, doi: 10.1063/1.1825077) makes large step simulations possible. Valuing functions are built and hedged using quantization and high dimensional interpolation methods. The hedging objective is taken to be capital minimization as described in Carr, Madan and Vicente Alvarez (2011, Markets, profits, capital, leverage and returns, Journal of Risk, 14, pp. 95-122).
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the variance Gamma Process and option pricing
Review of Finance, 1998Co-Authors: Dilip B Madan, Peter Carr, Eric C ChangAbstract:A three parameter stochastic Process, termed the variance Gamma Process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The Process is obtained by evaluating Brownian motion with drift at a random time given by a Gamma Process. The two additional parameters are the drift of the Brownian motion and the volatility of the time change. These additional parameters provide control over the skewness and kurtosis of the return distribution. Closed forms are obtained for the return density and the prices of European options. The statistical and risk neutral densities are estimated for data on the S&P500 Index and the prices of options on this Index. It is observed that the statistical density is symmetric with some kurtosis, while the risk neutral density is negatively skewed with a larger kurtosis. The additional parameters also correct for pricing biases of the Black Scholes model that is a parametric special case of the option pricing model developed here.
