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Constrained Stochastic Recursive Linear Quadratic Optimal Control Problems and Application to Finance
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-024-1157-9
Liang-quan Zhang, Qing Zhou
{"title":"Constrained Stochastic Recursive Linear Quadratic Optimal Control Problems and Application to Finance","authors":"Liang-quan Zhang,&nbsp;Qing Zhou","doi":"10.1007/s10255-024-1157-9","DOIUrl":"10.1007/s10255-024-1157-9","url":null,"abstract":"<div><p>In this paper, we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation (BSDE in short) with deterministic coefficients. One of the significant features in this framework, in contrast to the classical LQ issue, embodies that the admissible control set needs to satisfy more than the square integrability. By introducing two kinds of new generalized Riccati equations, we are able to announce the explicit optimal control and the solution to the corresponding H-J-B equation. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result with short-selling prohibited. Feasibility of the mean-variance portfolio selection problem via BSDE for a financial market is characterized, and associated efficient portfolios are given in a closed form.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"375 - 399"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Improved accuracy of an analytical approximation for option pricing under stochastic volatility models using deep learning techniques
IF 2.9 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-04-02 DOI: 10.1016/j.camwa.2025.03.029
Donghyun Kim , Jeonggyu Huh , Ji-Hun Yoon
{"title":"Improved accuracy of an analytical approximation for option pricing under stochastic volatility models using deep learning techniques","authors":"Donghyun Kim ,&nbsp;Jeonggyu Huh ,&nbsp;Ji-Hun Yoon","doi":"10.1016/j.camwa.2025.03.029","DOIUrl":"10.1016/j.camwa.2025.03.029","url":null,"abstract":"<div><div>This paper addresses the challenge of pricing options under stochastic volatility (SV) models, where explicit formulae are often unavailable and parameter estimation requires extensive numerical simulations. Traditional approaches typically either rely on large volumes of historical (option) data (data-driven methods) or generate synthetic prices across wide parameter grids (model-driven methods). In both cases, the scale of data demands can be prohibitively high. We propose an alternative strategy that trains a neural network on the <em>residuals</em> between a fast but approximate pricing formula and numerically generated option prices, rather than learning the full pricing function directly. Focusing on these smaller, smoother residuals notably reduces the complexity of the learning task and lowers data requirements. We further demonstrate theoretically that the Rademacher complexity of the residual function class is significantly smaller, thereby improving generalization with fewer samples. Numerical experiments on fast mean-reverting SV models show that our residual-learning framework achieves accuracy comparable to baseline networks but uses only about one-tenth the training data. These findings highlight the potential of residual-based neural approaches to deliver efficient, accurate pricing and facilitate practical calibration of advanced SV models.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 150-165"},"PeriodicalIF":2.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniqueness and Nondegeneracy of Positive Solutions of General Kirchhoff Type Equations
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-023-1062-7
Yu-ting Kang, Peng Luo, Chang-lin Xiang, Xue-xiu Zhong
{"title":"Uniqueness and Nondegeneracy of Positive Solutions of General Kirchhoff Type Equations","authors":"Yu-ting Kang,&nbsp;Peng Luo,&nbsp;Chang-lin Xiang,&nbsp;Xue-xiu Zhong","doi":"10.1007/s10255-023-1062-7","DOIUrl":"10.1007/s10255-023-1062-7","url":null,"abstract":"<div><p>In the present paper, we study uniqueness and nondegeneracy of positive solutions to the general Kirchhoff type equations </p><div><div><span>$$-Mleft(int_{mathbb{R}^{N}}{vertnabla vvert}^{2}dxright)Delta v=g(v) quad {rm in};{mathbb{R}^{N}},$$</span></div></div><p> where <i>M</i>: [0, +∞) ↦ ℝ is a continuous function satisfying some suitable conditions and <i>v</i> ∈ <i>H</i><sup>1</sup>(ℝ<sup><i>N</i></sup>). Applying our results to the case <i>M</i>(<i>t</i>) = <i>at</i> + <i>b, a, b</i> &gt; 0, we make it clear all the positive solutions for all dimensions <i>N</i> ≥ 1. Our results can be viewed as a generalization of the corresponding results of Li et al. [JDE, 2020, 268, Section 1.2].</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"414 - 424"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Regularization Smoothing Newton Method for the Symmetric Cone Complementarity Problem with the Cartesian P0-property
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-025-0007-8
Xiang-jing Liu, San-yang Liu
{"title":"A Regularization Smoothing Newton Method for the Symmetric Cone Complementarity Problem with the Cartesian P0-property","authors":"Xiang-jing Liu,&nbsp;San-yang Liu","doi":"10.1007/s10255-025-0007-8","DOIUrl":"10.1007/s10255-025-0007-8","url":null,"abstract":"<div><p>In this paper, we consider the symmetric cone linear complementarity problem with the Cartesian <i>P</i><sub>0</sub>-property and present a regularization smoothing method with a nonmonotone line search to solve this problem. It has been demonstrated that the proposed method exhibits global convergence under the condition that the solution set of the complementarity problem is nonempty. This condition is less stringent than those that have appeared in some existing literature. We also show that the method has locally quadratic convergence under appropriate conditions. Some experimental results are reported to illustrate the efficiency of the proposed method.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"556 - 572"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global Existence and Boundedness for the Attraction-repulsion Keller-Segel Model with Volume Filling Effect
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-025-0020-y
Jian Deng
{"title":"Global Existence and Boundedness for the Attraction-repulsion Keller-Segel Model with Volume Filling Effect","authors":"Jian Deng","doi":"10.1007/s10255-025-0020-y","DOIUrl":"10.1007/s10255-025-0020-y","url":null,"abstract":"<div><p>This paper is concerned with the attraction-repulsion Keller-Segel model with volume filling effect. We consider this problem in a bounded domain Ω ⊂ ℝ<sup>3</sup> under zero-flux boundary condition, and it is shown that the volume filling effect will prevent overcrowding behavior, and no blow up phenomenon happen. In fact, we show that for any initial datum, the problem admits a unique global-in-time classical solution, which is bounded uniformly. Previous findings for the chemotaxis model with volume filling effect were derived under the assumption 0 ≤ <i>u</i><sub>0</sub>(<i>x</i>) ≤ 1 with <i>ρ</i>(<i>x,t</i>) ≡ 1. However, when the maximum size of the aggregate is not a constant but rather a function <i>ρ</i>(<i>x,t</i>), ensuring the boundedness of the solutions becomes significantly challenging. This introduces a fundamental difficulty into the analysis.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"513 - 524"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Lindley-Weibull Distribution
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-025-0003-z
Jun-mei Jia, Zai-zai Yan, Xiu-yun Peng
{"title":"The Lindley-Weibull Distribution","authors":"Jun-mei Jia,&nbsp;Zai-zai Yan,&nbsp;Xiu-yun Peng","doi":"10.1007/s10255-025-0003-z","DOIUrl":"10.1007/s10255-025-0003-z","url":null,"abstract":"<div><p>In this paper, a new distribution named the Lindley-Weibull distribution which combines Lindley and Weibull distributions by using the method of T-X family is introduced. This distribution offers a more flexible model for lifetime data. We study its statistical properties include the shapes of density and hazard rate, residual and reversed residual lifetime, moment, moment generating functions, conditional moment, conditional moment generating, quantiles functions, mean deviations, Rényi entropy, Bonferroni and Loren curves. The distribution is capable of modeling increasing, decreasing, upside-down bathtub and decreasing-increasing-decreasing hazard rate functions. The method of maximum likelihood is adopted for estimating the model parameters. The potentiality of the new model is illustrated by means of one real data set.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"588 - 600"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Equivariant birational geometry of cubic fourfolds and derived categories
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2025-04-02 DOI: 10.1016/j.aim.2025.110249
Christian Böhning , Hans-Christian Graf von Bothmer , Yuri Tschinkel
{"title":"Equivariant birational geometry of cubic fourfolds and derived categories","authors":"Christian Böhning ,&nbsp;Hans-Christian Graf von Bothmer ,&nbsp;Yuri Tschinkel","doi":"10.1016/j.aim.2025.110249","DOIUrl":"10.1016/j.aim.2025.110249","url":null,"abstract":"<div><div>We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"469 ","pages":"Article 110249"},"PeriodicalIF":1.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Josephson “flying qubit” revival: Flux-based control optimization
IF 5.3 1区 数学
Chaos Solitons & Fractals Pub Date : 2025-04-02 DOI: 10.1016/j.chaos.2025.116353
M.V. Bastrakova , D.S. Pashin , P.V. Pikunov , I.I. Soloviev , A.E. Schegolev , N.V. Klenov
{"title":"Josephson “flying qubit” revival: Flux-based control optimization","authors":"M.V. Bastrakova ,&nbsp;D.S. Pashin ,&nbsp;P.V. Pikunov ,&nbsp;I.I. Soloviev ,&nbsp;A.E. Schegolev ,&nbsp;N.V. Klenov","doi":"10.1016/j.chaos.2025.116353","DOIUrl":"10.1016/j.chaos.2025.116353","url":null,"abstract":"<div><div>A decade ago, Josephson “flying qubits” based on adiabatic superconducting logic cells showed promise as quantum data buses, but their development stalled due to the incompatibility of traditional qubit control methods with their design. We revisit this concept by exploring the control of the inductively shunted two-junction superconducting interferometer (adiabatic quantum flux parametron, AQFP) in the quantum regime using unipolar magnetic field pulses generated by adiabatic superconducting electronics. Our research demonstrates the feasibility of high fidelity quantum operations (fidelity more than 99.99%) in this system via Landau–Zener tunneling. To this end, a method is proposed for selecting the duration and shape of control pulses to eliminate unwanted leakage into high-lying states in AQFP-based systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116353"},"PeriodicalIF":5.3,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local terms for the categorical trace
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2025-04-02 DOI: 10.1016/j.aim.2025.110223
Dennis Gaitsgory , Yakov Varshavsky
{"title":"Local terms for the categorical trace","authors":"Dennis Gaitsgory ,&nbsp;Yakov Varshavsky","doi":"10.1016/j.aim.2025.110223","DOIUrl":"10.1016/j.aim.2025.110223","url":null,"abstract":"<div><div>In this paper we introduce the categorical “true local terms” maps for Artin stacks and show that they are additive and commute with proper pushforwards, smooth pullbacks and specializations. In particular, we generalizing results of <span><span>[14]</span></span> to this setting.</div><div>As an application, we supply proofs of two theorems stated in <span><span>[1]</span></span>. Namely, we show that the “true local terms” of the Frobenius endomorphism coincide with the “naive local terms” and that the “naive local terms” commute with !-pushforwards. The latter result is a categorical version of the classical Grothendieck–Lefschetz trace formula.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110223"},"PeriodicalIF":1.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Suppression of blow-up in 3-D Keller-Segel model via the Couette flow in whole space
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-04-02 DOI: 10.1016/j.jde.2025.113265
Shijin Deng , Binbin Shi , Weike Wang
{"title":"Suppression of blow-up in 3-D Keller-Segel model via the Couette flow in whole space","authors":"Shijin Deng ,&nbsp;Binbin Shi ,&nbsp;Weike Wang","doi":"10.1016/j.jde.2025.113265","DOIUrl":"10.1016/j.jde.2025.113265","url":null,"abstract":"<div><div>In this paper, we study the 3-D parabolic-parabolic and parabolic-elliptic Keller-Segel models with the Couette flow. We prove that the blow-up phenomenon of solution can be suppressed by enhanced dissipation of the large Couette flows. Here we develop Green's function method to describe the enhanced dissipation via a more precise space-time structure and obtain the global existence together with pointwise estimates of the solutions. The result of this paper shows that the enhanced dissipation exists for all frequencies in the case of whole space and it is the reason that we obtain global existence for 3-D Keller-Segel models here. It is totally different from the case with the periodic spatial variable <em>x</em> in <span><span>[3]</span></span>, <span><span>[10]</span></span>. This paper provides a new methodology to capture dissipation enhancement and also a surprising result which shows a totally new mechanism.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"432 ","pages":"Article 113265"},"PeriodicalIF":2.4,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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