Mathematical Finance最新文献_第7页

Reinforcement learning with dynamic convex risk measures 动态凸风险度量的强化学习

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-04-17 DOI: 10.1111/mafi.12388

Anthony Coache, Sebastian Jaimungal

引用次数: 0

Trading with the crowd 与人群交易

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-04-11 DOI: 10.1111/mafi.12390

Eyal Neuman, Moritz Voß

{"title":"Trading with the crowd","authors":"Eyal Neuman, Moritz Voß","doi":"10.1111/mafi.12390","DOIUrl":"10.1111/mafi.12390","url":null,"abstract":"We formulate and solve a multi-player stochastic differential game between financial agents who seek to cost-efficiently liquidate their position in a risky asset in the presence of jointly aggregated transient price impact, along with taking into account a common general price predicting signal. The unique Nash-equilibrium strategies reveal how each agent's liquidation policy adjusts the predictive trading signal to the aggregated transient price impact induced by all other agents. This unfolds a quantitative relation between trading signals and the order flow in crowded markets. We also formulate and solve the corresponding mean field game in the limit of infinitely many agents. We prove that the equilibrium trading speed and the value function of an agent in the finite N-player game converges to the corresponding trading speed and value function in the mean field game at rate <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>O</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>N</mi>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$O(N^{-2})$</annotation>\u0000 </semantics></math>. In addition, we prove that the mean field optimal strategy provides an approximate Nash-equilibrium for the finite-player game.","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"33 3","pages":"548-617"},"PeriodicalIF":1.6,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12390","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45517220","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: 12

Recent advances in reinforcement learning in finance 金融强化学习的最新进展

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-04-07 DOI: 10.1111/mafi.12382

Ben Hambly, Renyuan Xu, Huining Yang

{"title":"Recent advances in reinforcement learning in finance","authors":"Ben Hambly, Renyuan Xu, Huining Yang","doi":"10.1111/mafi.12382","DOIUrl":"10.1111/mafi.12382","url":null,"abstract":"The rapid changes in the finance industry due to the increasing amount of data have revolutionized the techniques on data processing and data analysis and brought new theoretical and computational challenges. In contrast to classical stochastic control theory and other analytical approaches for solving financial decision-making problems that heavily reply on model assumptions, new developments from reinforcement learning (RL) are able to make full use of the large amount of financial data with fewer model assumptions and to improve decisions in complex financial environments. This survey paper aims to review the recent developments and use of RL approaches in finance. We give an introduction to Markov decision processes, which is the setting for many of the commonly used RL approaches. Various algorithms are then introduced with a focus on value- and policy-based methods that do not require any model assumptions. Connections are made with neural networks to extend the framework to encompass deep RL algorithms. We then discuss in detail the application of these RL algorithms in a variety of decision-making problems in finance, including optimal execution, portfolio optimization, option pricing and hedging, market making, smart order routing, and robo-advising. Our survey concludes by pointing out a few possible future directions for research.","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"33 3","pages":"437-503"},"PeriodicalIF":1.6,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12382","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47028350","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: 60

Analytical solvability and exact simulation in models with affine stochastic volatility and Lévy jumps 仿射随机波动和lsamvy跳变模型的解析可解性和精确模拟

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-04-05 DOI: 10.1111/mafi.12387

Pingping Zeng, Ziqing Xu, Pingping Jiang, Yue Kuen Kwok

引用次数: 3

Equilibria of time-inconsistent stopping for one-dimensional diffusion processes 一维扩散过程的时间不一致停止平衡

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-04-03 DOI: 10.1111/mafi.12385

Erhan Bayraktar, Zhenhua Wang, Zhou Zhou

引用次数: 8

Credit risk pricing in a consumption-based equilibrium framework with incomplete accounting information 不完全会计信息下消费均衡框架下的信用风险定价

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-04-03 DOI: 10.1111/mafi.12386

Junchi Ma, Mobolaji Ogunsolu, Jinniao Qiu, Ayşe Deniz Sezer

{"title":"Credit risk pricing in a consumption-based equilibrium framework with incomplete accounting information","authors":"Junchi Ma, Mobolaji Ogunsolu, Jinniao Qiu, Ayşe Deniz Sezer","doi":"10.1111/mafi.12386","DOIUrl":"10.1111/mafi.12386","url":null,"abstract":"We present a consumption-based equilibrium framework for credit risk pricing based on the Epstein–Zin (EZ) preferences where the default time is modeled as the first hitting time of a default boundary and bond investors have imperfect/partial information about the firm value. The imperfect information is generated by the underlying observed state variables and a noisy observation process of the firm value. In addition, the consumption, the volatility, and the firm value process are modeled to follow affine diffusion processes. Using the EZ equilibrium solution as the pricing kernel, we provide an equivalent pricing measure to compute the prices of financial derivatives as discounted values of the future payoffs given the incomplete information. The price of a zero-coupon bond is represented in terms of the solutions of a stochastic partial differential equation (SPDE) and a deterministic PDE; the self-contained proofs are provided for both this representation and the well-posedness of the involved SPDE. Furthermore, this SPDE is numerically solved, which yields some insights into the relationship between the structure of the yield spreads and the model parameters.","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"33 3","pages":"666-708"},"PeriodicalIF":1.6,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12386","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46688591","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: 1

Noncausal affine processes with applications to derivative pricing 非因果仿射过程及其在导数定价中的应用

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-03-31 DOI: 10.1111/mafi.12384

Christian Gouriéroux, Yang Lu

引用次数: 2

Effective algorithms for optimal portfolio deleveraging problem with cross impact 交叉影响下最优投资组合去杠杆问题的有效算法

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-03-30 DOI: 10.1111/mafi.12383

Hezhi Luo, Yuanyuan Chen, Xianye Zhang, Duan Li, Huixian Wu

{"title":"Effective algorithms for optimal portfolio deleveraging problem with cross impact","authors":"Hezhi Luo, Yuanyuan Chen, Xianye Zhang, Duan Li, Huixian Wu","doi":"10.1111/mafi.12383","DOIUrl":"10.1111/mafi.12383","url":null,"abstract":"We investigate the optimal portfolio deleveraging (OPD) problem with permanent and temporary price impacts, where the objective is to maximize equity while meeting a prescribed debt/equity requirement. We take the real situation with cross impact among different assets into consideration. The resulting problem is, however, a nonconvex quadratic program with a quadratic constraint and a box constraint, which is known to be NP-hard. In this paper, we first develop a successive convex optimization (SCO) approach for solving the OPD problem and show that the SCO algorithm converges to a KKT point of its transformed problem. Second, we propose an effective global algorithm for the OPD problem, which integrates the SCO method, simple convex relaxation, and a branch-and-bound framework, to identify a global optimal solution to the OPD problem within a prespecified ε-tolerance. We establish the global convergence of our algorithm and estimate its complexity. We also conduct numerical experiments to demonstrate the effectiveness of our proposed algorithms with both real data and randomly generated medium- and large-scale OPD instances.","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 1","pages":"36-89"},"PeriodicalIF":1.6,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42650971","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: 3

A general approximation method for optimal stopping and random delay 最优停车和随机延迟的一般近似方法

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-03-20 DOI: 10.1111/mafi.12380

Pengzhan Chen, Yingda Song

引用次数: 0

Markov decision processes under model uncertainty 模型不确定性下的马尔可夫决策过程

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-03-17 DOI: 10.1111/mafi.12381

Ariel Neufeld, Julian Sester, Mario Šikić

{"title":"Markov decision processes under model uncertainty","authors":"Ariel Neufeld, Julian Sester, Mario Šikić","doi":"10.1111/mafi.12381","DOIUrl":"10.1111/mafi.12381","url":null,"abstract":"We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle, we obtain a local-to-global paradigm, namely solving a local, that is, a one time-step robust optimization problem leads to an optimizer of the global (i.e., infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure. Moreover, we apply this framework to portfolio optimization involving data of the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mo>&</mo>\u0000 <mi>P</mi>\u0000 <mspace></mspace>\u0000 <mn>500</mn>\u0000 </mrow>\u0000 <annotation>$S&Pnobreakspace 500$</annotation>\u0000 </semantics></math>. We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account.","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"33 3","pages":"618-665"},"PeriodicalIF":1.6,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43218515","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: 5