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Mathematical Finance最新文献

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Special issue on machine learning in finance 金融领域的机器学习特刊
IF 1.6 3区 经济学
Mathematical Finance Pub Date : 2024-02-13 DOI: 10.1111/mafi.12430
Christa Cuchiero, Ruimeng Hu, Sara Svaluto-Ferro, Renyuan Xu
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引用次数: 0
Special issue on machine learning in finance 金融领域的机器学习特刊
IF 1.6 3区 经济学
Mathematical Finance Pub Date : 2024-02-13 DOI: 10.1111/mafi.12430
Christa Cuchiero, Ruimeng Hu, Sara Svaluto-Ferro, Renyuan Xu
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引用次数: 0
Naïve Markowitz policies 天真马科维茨政策
IF 1.6 3区 经济学
Mathematical Finance Pub Date : 2024-02-13 DOI: 10.1111/mafi.12431
Lin Chen, Xun Yu Zhou
{"title":"Naïve Markowitz policies","authors":"Lin Chen,&nbsp;Xun Yu Zhou","doi":"10.1111/mafi.12431","DOIUrl":"10.1111/mafi.12431","url":null,"abstract":"<p>We study a continuous-time Markowitz mean–variance portfolio selection model in which a naïve agent, unaware of the underlying time-inconsistency, continuously reoptimizes over time. We define the resulting naïve policies through the limit of discretely naïve policies that are committed only in very small time intervals, and derive them analytically and explicitly. We compare naïve policies with pre-committed optimal policies and with consistent planners' equilibrium policies in a Black–Scholes market, and find that the former achieve higher expected terminal returns than originally planned yet are mean–variance inefficient when the risk aversion level is sufficiently small, and always take strictly riskier exposure than equilibrium policies. We finally define an efficiency ratio for comparing return–risk tradeoff with the same original level of risk aversion, and show that naïve policies are always strictly less efficient than pre-committed and equilibrium policies.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139950003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mean-field liquidation games with market drop-out 有市场退出的平均场清算博弈
IF 1.6 3区 经济学
Mathematical Finance Pub Date : 2024-01-15 DOI: 10.1111/mafi.12429
Guanxing Fu, Paul P. Hager, Ulrich Horst
{"title":"Mean-field liquidation games with market drop-out","authors":"Guanxing Fu,&nbsp;Paul P. Hager,&nbsp;Ulrich Horst","doi":"10.1111/mafi.12429","DOIUrl":"10.1111/mafi.12429","url":null,"abstract":"<p>We consider a novel class of portfolio liquidation games with market drop-out (“absorption”). More precisely, we consider mean-field and finite player liquidation games where a player drops out of the market when her position hits zero. In particular, round-trips are not admissible. This can be viewed as a no statistical arbitrage condition. In a model with only sellers, we prove that the absorption condition is equivalent to a short selling constraint. We prove that equilibria (both in the mean-field and the finite player game) are given as solutions to a nonlinear higher-order integral equation with endogenous terminal condition. We prove the existence of a unique solution to the integral equation from which we obtain the existence of a unique equilibrium in the MFG and the existence of a unique equilibrium in the <i>N</i>-player game. We establish the convergence of the equilibria in the finite player games to the obtained mean-field equilibrium and illustrate the impact of the drop-out constraint on equilibrium trading rates.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139481058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Almost strong equilibria for time-inconsistent stopping problems under finite horizon in continuous time 连续时间有限视野下时间不一致停止问题的近强均衡
IF 1.6 3区 经济学
Mathematical Finance Pub Date : 2023-12-25 DOI: 10.1111/mafi.12428
Zhou Zhou
{"title":"Almost strong equilibria for time-inconsistent stopping problems under finite horizon in continuous time","authors":"Zhou Zhou","doi":"10.1111/mafi.12428","DOIUrl":"10.1111/mafi.12428","url":null,"abstract":"<p>We consider time-inconsistent stopping problems for a continuous-time Markov chain under finite time horizon with non-exponential discounting. We provide an example indicating that strong equilibria may not exist in general. As a result, we propose a notion of equilibrium called almost strong equilibrium (ASE), which is a weak equilibrium and satisfies the condition of strong equilibria except at the boundary points of the associated stopping region. We provide an iteration procedure and show that this procedure leads to an ASE. Moreover, we prove that this ASE is the unique ASE among all regular stopping policies under finite horizon <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>&lt;</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$T&amp;lt;infty$</annotation>\u0000 </semantics></math>. In contrast, we show that strong equilibria (and thus ASE) exist and may not be unique for the infinite horizon case <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>=</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$T=infty$</annotation>\u0000 </semantics></math>. Furthermore, we show that the limit of the finite-horizon ASE as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$Trightarrow infty$</annotation>\u0000 </semantics></math> is a weak equilibrium for the infinite-horizon problem, and may not be a strong equilibrium or ASE.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12428","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139035134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
GANs training: A game and stochastic control approach GANs 训练：博弈与随机控制方法
IF 1.6 3区 经济学
Mathematical Finance Pub Date : 2023-12-18 DOI: 10.1111/mafi.12427
Xin Guo, Othmane Mounjid
{"title":"GANs training: A game and stochastic control approach","authors":"Xin Guo,&nbsp;Othmane Mounjid","doi":"10.1111/mafi.12427","DOIUrl":"10.1111/mafi.12427","url":null,"abstract":"<p>Training generative adversarial networks (GANs) are known to be difficult, especially for financial time series. This paper first analyzes the well-posedness problem in GANs minimax games and the widely recognized convexity issue in GANs objective functions. It then proposes a stochastic control framework for hyper-parameters tuning in GANs training. The weak form of dynamic programming principle and the uniqueness and the existence of the value function in the viscosity sense for the corresponding minimax game are established. In particular, explicit forms for the optimal adaptive learning rate and batch size are derived and are shown to depend on the convexity of the objective function, revealing a relation between improper choices of learning rate and explosion in GANs training. Finally, empirical studies demonstrate that training algorithms incorporating this adaptive control approach outperform the standard ADAM method in terms of convergence and robustness. From GANs training perspective, the analysis in this paper provides analytical support for the popular practice of “clipping,” and suggests that the convexity and well-posedness issues in GANs may be tackled through appropriate choices of hyper-parameters.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138823991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations 随机微分方程平稳分布上的连续时间随机梯度下降优化
IF 1.6 3区 经济学
Mathematical Finance Pub Date : 2023-11-27 DOI: 10.1111/mafi.12422
Ziheng Wang, Justin Sirignano
{"title":"Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations","authors":"Ziheng Wang,&nbsp;Justin Sirignano","doi":"10.1111/mafi.12422","DOIUrl":"10.1111/mafi.12422","url":null,"abstract":"<p>We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an estimate for the gradient of the stationary distribution. The gradient estimate is simultaneously updated using forward propagation of the SDE state derivatives, asymptotically converging to the direction of steepest descent. We rigorously prove convergence of the online forward propagation algorithm for linear SDE models (i.e., the multidimensional Ornstein–Uhlenbeck process) and present its numerical results for nonlinear examples. The proof requires analysis of the fluctuations of the parameter evolution around the direction of steepest descent. Bounds on the fluctuations are challenging to obtain due to the online nature of the algorithm (e.g., the stationary distribution will continuously change as the parameters change). We prove bounds for the solutions of a new class of Poisson partial differential equations (PDEs), which are then used to analyze the parameter fluctuations in the algorithm. Our algorithm is applicable to a range of mathematical finance applications involving statistical calibration of SDE models and stochastic optimal control for long time horizons where ergodicity of the data and stochastic process is a suitable modeling framework. Numerical examples explore these potential applications, including learning a neural network control for high-dimensional optimal control of SDEs and training stochastic point process models of limit order book events.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Time-inconsistent contract theory 时间不一致契约理论
IF 1.6 3区 经济学
Mathematical Finance Pub Date : 2023-11-24 DOI: 10.1111/mafi.12426
Camilo Hernández, Dylan Possamaï
{"title":"Time-inconsistent contract theory","authors":"Camilo Hernández,&nbsp;Dylan Possamaï","doi":"10.1111/mafi.12426","DOIUrl":"10.1111/mafi.12426","url":null,"abstract":"<p>This paper investigates the moral hazard problem in finite horizon with both continuous and lump-sum payments, involving a time-inconsistent sophisticated agent and a standard utility maximizer principal: Building upon the so-called dynamic programming approach in Cvitanić et al. (2018) and the recently available results in Hernández and Possamaï (2023), we present a methodology that covers the previous contracting problem. Our main contribution consists of a characterization of the moral hazard problem faced by the principal. In particular, it shows that under relatively mild technical conditions on the data of the problem, the supremum of the principal's expected utility over a smaller restricted family of contracts is equal to the supremum over all feasible contracts. Nevertheless, this characterization yields, as far as we know, a novel class of control problems that involve the control of a forward Volterra equation via Volterra-type controls, and infinite-dimensional stochastic target constraints. Despite the inherent challenges associated with such a problem, we study the solution under three different specifications of utility functions for both the agent and the principal, and draw qualitative implications from the form of the optimal contract. The general case remains the subject of future research. We illustrate some of our results in the context of a project selection contracting problem between an investor and a time-inconsistent manager.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12426","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138536735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantifying dimensional change in stochastic portfolio theory 随机投资组合理论中量纲变化的量化
IF 1.6 3区 经济学
Mathematical Finance Pub Date : 2023-11-19 DOI: 10.1111/mafi.12425
Erhan Bayraktar, Donghan Kim, Abhishek Tilva
{"title":"Quantifying dimensional change in stochastic portfolio theory","authors":"Erhan Bayraktar,&nbsp;Donghan Kim,&nbsp;Abhishek Tilva","doi":"10.1111/mafi.12425","DOIUrl":"10.1111/mafi.12425","url":null,"abstract":"<p>In this paper, we develop the theory of functional generation of portfolios in an equity market with changing dimension. By introducing dimensional jumps in the market, as well as jumps in stock capitalization between the dimensional jumps, we construct different types of self-financing stock portfolios (additive, multiplicative, and rank-based) in a very general setting. Our study explains how a dimensional change caused by a listing or delisting event of a stock, and unexpected shocks in the market, affect portfolio return. We also provide empirical analyses of some classical portfolios, quantifying the impact of dimensional change in portfolio performance relative to the market.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12425","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138536785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Editorial: Special Issue for the 11th World Congress of the Bachelier Finance Society 社论：巴切利耶金融学会第 11 届世界大会特刊
IF 1.6 3区 经济学
Mathematical Finance Pub Date : 2023-11-13 DOI: 10.1111/mafi.12424
Nan Chen, Xunyu Zhou
{"title":"Editorial: Special Issue for the 11th World Congress of the Bachelier Finance Society","authors":"Nan Chen,&nbsp;Xunyu Zhou","doi":"10.1111/mafi.12424","DOIUrl":"https://doi.org/10.1111/mafi.12424","url":null,"abstract":"","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139110072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","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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