The Experts below are selected from a list of 534 Experts worldwide ranked by ideXlab platform
Rodin, Aleksei S. - One of the best experts on this subject based on the ideXlab platform.
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ON THE STRUCTURE OF THE SINGULAR SET OF A PIECEWISE SMOOTH MINIMAX SOLUTION OF THE HAMILTON–JACOBI–BELLMAN EQUATION
'Ural Federal University', 2016Co-Authors: Rodin, Aleksei S.Abstract:The properties of a minimax piecewise smooth solution of the Hamilton–Jacobi–Bellman equation are studied. It is known the Rankine–Hugoniot conditions are necessary and sufficient conditions for the points of Nondifferentiability (singularity) of the minimax solution. We generalize this condition and describe the dimension of smooth manifolds contained in the singular set of the piecewise smooth solution in terms of state characteristics that come to this set. New structural properties of the singular set are obtained in the case where the Hamiltonian depends only on the impulse variable
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On the Structure of the Singular Set of a Piecewise Smooth Minimax Solution of the Hamilton–Jacobi–Bellman Equation
'Ural Federal University', 2016Co-Authors: Rodin, Aleksei S.Abstract:The properties of a minimax piecewise smooth solution of the Hamilton–Jacobi–Bellman equation are studied. It is known the Rankine–Hugoniot conditions are necessary and sufficient conditions for the points of Nondifferentiability (singularity) of the minimax solution. We generalize this condition and describe the dimension of smooth manifolds contained in the singular set of the piecewise smooth solution in terms of state characteristics that come to this set. New structural properties of the singular set are obtained in the case where the Hamiltonian depends only on the impulse variable.This work was supported by the Russian Foundation for Basic Research (project no. 14-01-00168) and by the Program of the Presidium of the Russian Academy of Sciences "Mathematical Problems of Contemporary Control Theory" (project no. 387-2015-0075)
Somayeh Moazeni - One of the best experts on this subject based on the ideXlab platform.
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Smoothing and parametric rules for stochastic mean-CVaR optimal execution strategy
Annals of Operations Research, 2016Co-Authors: Somayeh Moazeni, Thomas F. Coleman, Yuying LiAbstract:Computing optimal stochastic portfolio execution strategies under an appropriate risk consideration presents many computational challenges. Using Monte Carlo simulations, we investigate an approach based on smoothing and parametric rules to minimize mean and Conditional Value-at-Risk (CVaR) of the execution cost. The proposed approach reduces computational complexity by smoothing the Nondifferentiability arising from the simulation discretization and by employing a parametric representation of a stochastic strategy. We further handle constraints using a smoothed exact penalty function. Using the downside risk as an example, we show that the proposed approach can be generalized to other risk measures. In addition, we computationally illustrate the effect of including risk on the stochastic optimal execution strategy.
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DOI 10.1007/s10479-013-1391-7 Smoothing and parametric rules for stochastic mean-CVaR optimal execution strategy
2016Co-Authors: Ann Oper Res, Somayeh Moazeni, Thomas F. ColemanAbstract:Abstract Computing optimal stochastic portfolio execution strategies under an appropriate risk consideration presents many computational challenges. Using Monte Carlo simulations, we investigate an approach based on smoothing and parametric rules to minimize mean and Conditional Value-at-Risk (CVaR) of the execution cost. The proposed approach reduces computational complexity by smoothing the Nondifferentiability arising from the simulation discretization and by employing a parametric representation of a stochastic strategy. We fur-ther handle constraints using a smoothed exact penalty function. Using the downside risk as an example, we show that the proposed approach can be generalized to other risk mea-sures. In addition, we computationally illustrate the effect of including risk on the stochastic optimal execution strategy
Sergey A Kamenshchikov - One of the best experts on this subject based on the ideXlab platform.
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transport catastrophe analysis as an alternative to a monofractal description theory and application to financial crisis time series
Journal of Chaos, 2014Co-Authors: Sergey A KamenshchikovAbstract:The goal of this investigation was to overcome limitations of a persistency analysis, introduced by Benoit Mandelbrot for monofractal Brownian processes: Nondifferentiability, Brownian nature of process, and a linear memory measure. We have extended a sense of a Hurst factor by consideration of a phase diffusion power law. It was shown that precatastrophic stabilization as an indicator of bifurcation leads to a new minimum of momentary phase diffusion, while bifurcation causes an increase of the momentary transport. An efficiency of a diffusive analysis has been experimentally compared to the Reynolds stability model application. An extended Reynolds parameter has been introduced as an indicator of phase transition. A combination of diffusive and Reynolds analyses has been applied for a description of a time series of Dow Jones Industrial weekly prices for the world financial crisis of 2007–2009. Diffusive and Reynolds parameters showed extreme values in October 2008 when a mortgage crisis was fixed. A combined R/D description allowed distinguishing of market evolution short-memory and long-memory shifts. It was stated that a systematic large scale failure of a financial system has begun in October 2008 and started fading in February 2009.
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transport catastrophe analysis as an alternative to a fractal description theory and application to financial crisis time series
arXiv: Statistical Finance, 2014Co-Authors: Sergey A KamenshchikovAbstract:The goal of this investigation was to overcome limitations of a persistency analysis, introduced by Benoit Mandelbrot for fractal Brownian processes: Nondifferentiability, Brownian nature of process and a linear memory measure. We have extended a sense of a Hurst factor by consideration of a phase diffusion power law. It was shown that pre-catastrophic stabilization as an indicator of bifurcation leads to a new minimum of momentary phase diffusion, while bifurcation causes an increase of the momentary transport. Basic conclusions of a diffusive analysis have been compared to the Lyapunov stability model. An extended Reynolds parameter has been introduces as an indicator of phase transition. A combination of diffusive and Reynolds analysis has been applied for a description of a time series of Dow Jones Industrial weekly prices for a world financial crisis of 2007-2009. Diffusive and Reynolds parameters shown an extreme values in October 2008 when a mortgage crisis was fixed. A combined R/D description allowed distinguishing of short-memory and long memory shifts of a market evolution. It was stated that a systematic large scale failure of a financial system has begun in October 2008 and started fading in February 2009.
Liva Ralaivola - One of the best experts on this subject based on the ideXlab platform.
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Multiple Indefinite Kernel Learning with Mixed Norm Regularization
2009Co-Authors: Matthieu Kowalski, Marie Szafranski, Liva RalaivolaAbstract:We address the problem of learning classifiers using several kernel functions. On the contrary to many contributions in the field of learning from different sources of information using kernels, we here do not assume that the kernels used are positive definite. The learning problem that we are interested in involves a misclassification loss term and a regularization term that is expressed by means of a mixed norm. The use of a mixed norm allows us to enforce some sparsity structure, a particular case of which is, for instance, the Group Lasso. We solve the convex problem by employing proximal minimization algorithms, which can be viewed as refined versions of gradient descent procedures capable of natu- rally dealing with Nondifferentiability. A numerical simulation on a UCI dataset shows the modularity of our approach.
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Author manuscript, published in "International Conference on Machine Learning (ICML 2009), Montreal: Canada (2009)" Multiple Indefinite Kernel Learning with Mixed Norm Regularization
2009Co-Authors: Matthieu Kowalski, Marie Szafranski, Liva RalaivolaAbstract:We address the problem of learning classifiers using several kernel functions. On the contrary to many contributions in the field of learning from different sources of information using kernels, we here do not assume that the kernels used are positive definite. The learning problem that we are interested in involves a misclassification loss term and a regularization term that is expressed by means of a mixed norm. The use of a mixed norm allows us to enforce some sparsity structure, a particular case of which is, for instance, the Group Lasso. We solve the convex problem by employing proximal minimization algorithms, which can be viewed as refined versions of gradient descent procedures capable of naturally dealing with Nondifferentiability. A numerical simulation on a UCI dataset shows the modularity of our approach. 1
Wei Zhang - One of the best experts on this subject based on the ideXlab platform.
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A Fast Adaptive Parameter Estimation for Total Variation Image Restoration
IEEE Transactions on Image Processing, 2014Co-Authors: Chuan He, Changhua Hu, Wei ZhangAbstract:Estimation of the regularization parameter, which strikes a balance between the data fidelity and regularity, is essential for successfully solving ill-posed image restoration problems. Based on the classical total variation (TV) model and prevalent alternating direction method of multipliers, we hammer out a fast algorithm being able to simultaneously estimate the regularization parameter and restore the degraded image. By applying variable splitting technique to both the regularization term and data fidelity term, we overcome the Nondifferentiability of TV and achieve a closed form to update the regularization parameter in each iteration. The solution is guaranteed to satisfy Morozov's discrepancy principle. Furthermore, we present a convergence proof for the proposed algorithm on the premise of a variable regularization parameter. Experimental results demonstrate that the proposed algorithm is superior in speed and competitive in accuracy compared with several state-of-the-art methods. Besides, the proposed method can be smoothly extended to the multichannel image restoration.