arXiv subjects

Jin Liang

Publications and source records attributed to Jin Liang.

6 recordsLinked to original sources

arXiv2024

Optimal Carbon Emission Control With Allowances Purchasing

In this paper, we consider a company can simultaneously reduce its emissions and buy carbon allowances at any time. We establish an optimal control model involving two stochastic processes with two control variables, which is a singular control problem. This model can then be converted into a Hamilton-Jacobi-Bellman (HJB) equation, which is a two-dimensional variational equality with gradient barrier, so that the free boundary is a surface. We prove the existence and uniqueness of the solution. Finally, some numerical results are shown.

math.OC↗

arXiv2023

Stability of traveling wave solutions in a credit rating migration Free Boundary Problem

In this paper, we study the stability of traveling wave solutions arising from a credit rating migration problem with a free boundary, After some transformations, we turn the Free Boundary Problem into a fully nonlinear parabolic problem on a fixed domain and establish a rigorous stability analysis of the equilibrium in an exponentially weighted function space. It implies the convergence of the discounted value of bonds that stands as an attenuated traveling wave solution.

math.AP↗

arXiv2023

4K-Resolution Photo Exposure Correction at 125 FPS with ~8K Parameters

The illumination of improperly exposed photographs has been widely corrected using deep convolutional neural networks or Transformers. Despite with promising performance, these methods usually suffer from large parameter amounts and heavy computational FLOPs on high-resolution photographs. In this paper, we propose extremely light-weight (with only ~8K parameters) Multi-Scale Linear Transformation (MSLT) networks under the multi-layer perception architecture, which can process 4K-resolution sRGB images at 125 Frame-Per-Second (FPS) by a Titan RTX GPU. Specifically, the proposed MSLT networks first decompose an input image into high and low frequency layers by Laplacian pyramid techniques, and then sequentially correct different layers by pixel-adaptive linear transformation, which is implemented by efficient bilateral grid learning or 1x1 convolutions. Experiments on two benchmark datasets demonstrate the efficiency of our MSLTs against the state-of-the-arts on photo exposure correction. Extensive ablation studies validate the effectiveness of our contributions. The code is available at https://github.com/Zhou-Yijie/MSLTNet.

cs.CV↗

arXiv2023

FCNet: A Convolutional Neural Network for Arbitrary-Length Exposure Estimation

The photographs captured by digital cameras usually suffer from over or under exposure problems. For image exposure enhancement, the tasks of Single-Exposure Correction (SEC) and Multi-Exposure Fusion (MEF) are widely studied in the image processing community. However, current SEC or MEF methods are developed under different motivations and thus ignore the internal correlation between SEC and MEF, making it difficult to process arbitrary-length sequences with improper exposures. Besides, the MEF methods usually fail at estimating the exposure of a sequence containing only under-exposed or over-exposed images. To alleviate these problems, in this paper, we develop a novel Fusion-Correction Network (FCNet) to tackle an arbitrary-length (including one) image sequence with improper exposures. This is achieved by fusing and correcting an image sequence by Laplacian Pyramid (LP) image decomposition. In each LP level, the low-frequency base component of the input image sequence is fed into a Fusion block and a Correction block sequentially for consecutive exposure estimation, implemented by alternative exposure fusion and correction. The exposure-corrected image in current LP level is upsampled and fused with the high-frequency detail components of the input image sequence in the next LP level, to output the base component for the Fusion and Correction blocks in next LP level. Experiments on the benchmark dataset demonstrate that our FCNet is effective on arbitrary-length exposure estimation, including both SEC and MEF. The code is publicly released at https://github.com/NKUJinLiang/FCNet.

eess.IV↗

arXiv2023

Double free boundary problem for defaultable corporate bond with credit rating migration risks and their asymptotic behaviors

In this work, a pricing model for a defaultable corporate bond with credit rating migration risk is established. The model turns out to be a free boundary problem with two free boundaries. The latter are the level sets of the solution but of different kinds. One is from the discontinuous second order term, the other from the obstacle. Existence, uniqueness, and regularity of the solution are obtained. We also prove that two free boundaries are $C^\infty$. The asymptotic behavior of the solution is also considered: we show that it converges to a traveling wave solution when time goes to infinity. Moreover, numerical results are presented.

math.AP↗

arXiv2017

Peierls-Bogolyubov's inequality for deformed exponentials

We study convexity or concavity of certain trace functions for the deformed logarithmic and exponential functions, and obtain in this way new trace inequalities for deformed exponentials that may be considered as generalizations of Peierls-Bogolyubov's inequality. We use these results to improve previously known lower bounds for the Tsallis relative entropy.

math-ph↗