arXiv - QuantFin - Mathematical Finance最新文献_第8页

Cooperation, Correlation and Competition in Ergodic $N$-player Games and Mean-field Games of Singular Controls: A Case Study 奇异控制的N$玩家博弈和平均场博弈中的合作、相关性和竞争：案例研究

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-04-23 DOI: arxiv-2404.15079

Federico Cannerozzi, Giorgio Ferrari

{"title":"Cooperation, Correlation and Competition in Ergodic $N$-player Games and Mean-field Games of Singular Controls: A Case Study","authors":"Federico Cannerozzi, Giorgio Ferrari","doi":"arxiv-2404.15079","DOIUrl":"https://doi.org/arxiv-2404.15079","url":null,"abstract":"We consider ergodic symmetric $N$-player and mean-field games of singular\u0000control in both cooperative and competitive settings. The state process\u0000dynamics of a representative player follow geometric Brownian motion,\u0000controlled additively through a nondecreasing process. Agents aim to maximize a\u0000long-time average reward functional with instantaneous profit of power type.\u0000The game shows strategic complementarities, in that the marginal profit\u0000function is increasing with respect to the dynamic average of the states of the\u0000other players, when $N<infty$, or with respect to the stationary mean of the\u0000players' distribution, in the mean-field case. In the mean-field formulation,\u0000we explicitly construct the solution to the mean-field control problem\u0000associated with central planner optimization, as well as Nash and coarse\u0000correlated equilibria (with singular and regular recommendations). Among our\u0000findings, we show that coarse correlated equilibria may exist even when Nash\u0000equilibria do not. Additionally, we show that a coarse correlated equilibrium\u0000with a regular (absolutely continuous) recommendation can outperform a Nash\u0000equilibrium where the equilibrium policy is of reflecting type (thus singularly\u0000continuous). Furthermore, we prove that the constructed mean-field control and\u0000mean-field equilibria can approximate the cooperative and competitive\u0000equilibria, respectively, in the corresponding game with $N$ players when $N$\u0000is sufficiently large. To the best of our knowledge, this paper is the first to\u0000characterize coarse correlated equilibria, construct the explicit solution to\u0000an ergodic mean-field control problem, and provide approximation results for\u0000the related $N$-player game in the context of singular control games.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140797839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Liquidity Pool Design on Automated Market Makers 自动做市商的流动性池设计

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-04-20 DOI: arxiv-2404.13291

Xue Dong He, Chen Yang, Yutian Zhou

引用次数: 0

BSDE-based stochastic control for optimal reinsurance in a dynamic contagion model 基于 BSDE 的随机控制，在动态传染模型中实现最优再保险

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-04-17 DOI: arxiv-2404.11482

Claudia Ceci, Alessandra Cretarola

{"title":"BSDE-based stochastic control for optimal reinsurance in a dynamic contagion model","authors":"Claudia Ceci, Alessandra Cretarola","doi":"arxiv-2404.11482","DOIUrl":"https://doi.org/arxiv-2404.11482","url":null,"abstract":"We investigate the optimal reinsurance problem in the risk model with jump\u0000clustering features introduced in [7]. This modeling framework is inspired by\u0000the concept initially proposed in [15], combining Hawkes and Cox processes with\u0000shot noise intensity models. Specifically, these processes describe\u0000self-exciting and externally excited jumps in the claim arrival intensity,\u0000respectively. The insurer aims to maximize the expected exponential utility of\u0000terminal wealth for general reinsurance contracts and reinsurance premiums. We\u0000discuss two different methodologies: the classical stochastic control approach\u0000based on the Hamilton-Jacobi-Bellman (HJB) equation and a backward stochastic\u0000differential equation (BSDE) approach. In a Markovian setting, differently from\u0000the classical HJB-approach, the BSDE method enables us to solve the problem\u0000without imposing any requirements for regularity on the associated value\u0000function. We provide a Verification Theorem in terms of a suitable BSDE driven\u0000by a two-dimensional marked point process and we prove an existence result\u0000relaying on the theory developed in [27] for stochastic Lipschitz generators.\u0000After discussing the optimal strategy for general reinsurance contracts and\u0000reinsurance premiums, we provide more explicit results in some relevant cases.\u0000Finally, we provide comparison results that highlight the heightened risk\u0000stemming from the self-exciting component in contrast to the externally-excited\u0000counterpart and discuss the monotonicity property of the value function.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Factor risk measures 因子风险测量

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-04-12 DOI: arxiv-2404.08475

Hirbod Assa, Peng Liu

引用次数: 0

Benchmark-Neutral Pricing 基准中立定价

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-04-09 DOI: arxiv-2407.01542

Eckhard Platen

引用次数: 0

Non-concave distributionally robust stochastic control in a discrete time finite horizon setting 离散时间有限视距背景下的非凹分布稳健随机控制

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-04-08 DOI: arxiv-2404.05230

Ariel Neufeld, Julian Sester

{"title":"Non-concave distributionally robust stochastic control in a discrete time finite horizon setting","authors":"Ariel Neufeld, Julian Sester","doi":"arxiv-2404.05230","DOIUrl":"https://doi.org/arxiv-2404.05230","url":null,"abstract":"In this article we present a general framework for non-concave\u0000distributionally robust stochastic control problems in a discrete time finite\u0000horizon setting. Our framework allows to consider a variety of different\u0000path-dependent ambiguity sets of probability measures comprising, as a natural\u0000example, the ambiguity set defined via Wasserstein-balls around path-dependent\u0000reference measures, as well as parametric classes of probability distributions.\u0000We establish a dynamic programming principle which allows to derive both\u0000optimal control and worst-case measure by solving recursively a sequence of\u0000one-step optimization problems. As a concrete application, we study the robust\u0000hedging problem of a financial derivative under an asymmetric (and non-convex)\u0000loss function accounting for different preferences of sell- and buy side when\u0000it comes to the hedging of financial derivatives. As our entirely data-driven\u0000ambiguity set of probability measures, we consider Wasserstein-balls around the\u0000empirical measure derived from real financial data. We demonstrate that during\u0000adverse scenarios such as a financial crisis, our robust approach outperforms\u0000typical model-based hedging strategies such as the classical Delta-hedging\u0000strategy as well as the hedging strategy obtained in the non-robust setting\u0000with respect to the empirical measure and therefore overcomes the problem of\u0000model misspecification in such critical periods.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"212 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalized measure Black-Scholes equation: Towards option self-similar pricing 广义计量布莱克-斯科尔斯方程：实现期权自相似定价

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-04-08 DOI: arxiv-2404.05214

Nizar Riane, Claire David

引用次数: 0

Watanabe's expansion: A Solution for the convexity conundrum 渡边扩展凸性难题的解决方案

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-04-01 DOI: arxiv-2404.01522

David García-Lorite, Raul Merino

引用次数: 0

From attention to profit: quantitative trading strategy based on transformer 从关注到盈利：基于变压器的量化交易策略

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-03-30 DOI: arxiv-2404.00424

Zhaofeng Zhang, Banghao Chen, Shengxin Zhu, Nicolas Langrené

{"title":"From attention to profit: quantitative trading strategy based on transformer","authors":"Zhaofeng Zhang, Banghao Chen, Shengxin Zhu, Nicolas Langrené","doi":"arxiv-2404.00424","DOIUrl":"https://doi.org/arxiv-2404.00424","url":null,"abstract":"In traditional quantitative trading practice, navigating the complicated and\u0000dynamic financial market presents a persistent challenge. Former machine\u0000learning approaches have struggled to fully capture various market variables,\u0000often ignore long-term information and fail to catch up with essential signals\u0000that may lead the profit. This paper introduces an enhanced transformer\u0000architecture and designs a novel factor based on the model. By transfer\u0000learning from sentiment analysis, the proposed model not only exploits its\u0000original inherent advantages in capturing long-range dependencies and modelling\u0000complex data relationships but is also able to solve tasks with numerical\u0000inputs and accurately forecast future returns over a period. This work collects\u0000more than 5,000,000 rolling data of 4,601 stocks in the Chinese capital market\u0000from 2010 to 2019. The results of this study demonstrated the model's superior\u0000performance in predicting stock trends compared with other 100 factor-based\u0000quantitative strategies with lower turnover rates and a more robust half-life\u0000period. Notably, the model's innovative use transformer to establish factors,\u0000in conjunction with market sentiment information, has been shown to enhance the\u0000accuracy of trading signals significantly, thereby offering promising\u0000implications for the future of quantitative trading strategies.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Limited Attention Allocation in a Stochastic Linear Quadratic System with Multiplicative Noise 带有乘法噪声的随机线性二次系统中的有限注意力分配

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-03-27 DOI: arxiv-2403.18528

Xiangyu Cui, Jianjun Gao, Lingjie Kong

引用次数: 0