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A mean field game approach to relative investment–consumption games with habit formation 用均值场博弈法研究习惯养成的相对投资-消费博弈
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-05-02 DOI: 10.1007/s11579-024-00360-4
Zongxia Liang, Keyu Zhang
{"title":"A mean field game approach to relative investment–consumption games with habit formation","authors":"Zongxia Liang, Keyu Zhang","doi":"10.1007/s11579-024-00360-4","DOIUrl":"https://doi.org/10.1007/s11579-024-00360-4","url":null,"abstract":"<p>This paper studies an optimal investment–consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as benchmarks to evaluate the performance of her decision. We formulate the <i>n</i>-agent game problems and the corresponding mean field game problems under the two utilities. One mean field equilibrium is derived in a closed form in each problem. In each problem with <i>n</i> agents, an approximate Nash equilibrium is then constructed using the obtained mean field equilibrium when <i>n</i> is sufficiently large. The explicit convergence order in each problem can also be obtained. In addition, we provide some numerical illustrations of our results.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"148 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140834706","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
Optimal bubble riding with price-dependent entry: a mean field game of controls with common noise 取决于价格的最佳泡沫进入：具有共同噪声的均值控制博弈
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-03-27 DOI: 10.1007/s11579-024-00353-3
Ludovic Tangpi, Shichun Wang
{"title":"Optimal bubble riding with price-dependent entry: a mean field game of controls with common noise","authors":"Ludovic Tangpi, Shichun Wang","doi":"10.1007/s11579-024-00353-3","DOIUrl":"https://doi.org/10.1007/s11579-024-00353-3","url":null,"abstract":"<p>In this paper we further extend the optimal bubble riding model proposed in Tangpi and Wang (Optimal bubble riding: a mean field game with varying entry times, 2022) by allowing for price-dependent entry times. Agents are characterized by their individual <i>entry threshold</i> that represents their belief in the strength of the bubble. Conversely, the growth dynamics of the bubble is fueled by the influx of players. Price-dependent entry naturally leads to a mean field game of controls with common noise and random entry time, for which we provide an existence result. The equilibrium is obtained by first solving discretized versions of the game in the weak formulation and then examining the measurability property in the limit. In this paper, the common noise comes from two sources: the price of the asset which all agents trade, and also the the exogenous bubble burst time, which we also discretize and incorporate into the model via progressive enlargement of filtration.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"13 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311522","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 ranking games with diffusion control 具有扩散控制的均场排位赛
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-03-26 DOI: 10.1007/s11579-024-00354-2
S. Ankirchner, N. Kazi-Tani, J. Wendt, C. Zhou
{"title":"Mean-field ranking games with diffusion control","authors":"S. Ankirchner, N. Kazi-Tani, J. Wendt, C. Zhou","doi":"10.1007/s11579-024-00354-2","DOIUrl":"https://doi.org/10.1007/s11579-024-00354-2","url":null,"abstract":"<p>We consider a stochastic differential game, where each player continuously controls the diffusion intensity of her own state process. The players must all choose from the same diffusion rate interval <span>([sigma _1, sigma _2])</span>, and have individual random time horizons that are independently drawn from the same distribution. The players whose states at their respective time horizons are among the best <span>(p in (0,1))</span> of all terminal states receive a fixed prize. We show that in the mean field version of the game there exists an equilibrium, where the representative player chooses the maximal diffusion rate when the state is below a given threshold, and the minimal rate else. The symmetric <i>n</i>-fold tuple of this threshold strategy is an approximate Nash equilibrium of the <i>n</i>-player game. Finally, we show that the more time a player has at her disposal, the higher her chances of winning.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"273 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299671","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
Capital risk, fiscal policy, and the distribution of wealth 资本风险、财政政策和财富分配
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-03-21 DOI: 10.1007/s11579-024-00359-x
Andrea Modena, Luca Regis
{"title":"Capital risk, fiscal policy, and the distribution of wealth","authors":"Andrea Modena, Luca Regis","doi":"10.1007/s11579-024-00359-x","DOIUrl":"https://doi.org/10.1007/s11579-024-00359-x","url":null,"abstract":"<p>We develop a dynamic model economy where self-employed entrepreneurs allocate their net worth to their firm capital and risk-less government bonds, facing borrowing constraints, uninsurable labour endowment and capital depreciation risk. We derive a numerical approximation of the model’s equilibrium and compare it with a benchmark economy with no capital risk. Unlike labour endowment risk, capital risk reduces aggregate capital accumulation and wages and generates a positive risk premium. Low- (high-) net-worth entrepreneurs, whose consumption depends primarily on labour (financial) income, hold higher (lower) capital risk exposure. These patterns exacerbate inequality by increasing the share of financially constrained individuals and fattening the tails of the net worth distribution. Fiscal policy affects these outcomes by redistributing resources and affecting the risk premium. Capital tax cuts benefit more low- or high-net-worth entrepreneurs, depending on whether taxes on bonds or labour income finance them.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"161 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201278","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
Opinion dynamics in communities with major influencers and implicit social influence via mean-field approximation 通过均值场近似研究具有主要影响者和隐性社会影响的社区中的舆论动态
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-03-18 DOI: 10.1007/s11579-024-00355-1
Delia Coculescu, Médéric Motte, Huyên Pham
{"title":"Opinion dynamics in communities with major influencers and implicit social influence via mean-field approximation","authors":"Delia Coculescu, Médéric Motte, Huyên Pham","doi":"10.1007/s11579-024-00355-1","DOIUrl":"https://doi.org/10.1007/s11579-024-00355-1","url":null,"abstract":"<p>We study binary opinion formation in a large population where individuals are influenced by the opinions of other individuals. The population is characterised by the existence of (i) communities where individuals share some similar features, (ii) opinion leaders that may trigger unpredictable opinion shifts in the short term (iii) some degree of incomplete information in the observation of the individual or public opinion processes. In this setting, we study three different approximate mechanisms: common sampling approximation, independent sampling approximation, and, what will be our main focus in this paper, McKean–Vlasov (or mean-field) approximation. We show that all three approximations perform well in terms of different metrics that we introduce for measuring population level and individual level errors. In the presence of a common noise represented by the major influencers opinions processes, and despite the absence of idiosyncratic noises, we derive a propagation of chaos type result. For the particular case of a linear model and particular specifications of the major influencers opinion dynamics, we provide additional analysis, including long term behavior and fluctuations of the public opinion. The theoretical results are complemented by some concrete examples and numerical analysis, illustrating the formation of echo-chambers, the propagation of chaos, and phenomena such as snowball effect and social inertia.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"123 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154083","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
The perturbation method applied to a robust optimization problem with constraint 将扰动法应用于带约束条件的稳健优化问题
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-03-18 DOI: 10.1007/s11579-024-00358-y
Peng Luo, Alexander Schied, Xiaole Xue
{"title":"The perturbation method applied to a robust optimization problem with constraint","authors":"Peng Luo, Alexander Schied, Xiaole Xue","doi":"10.1007/s11579-024-00358-y","DOIUrl":"https://doi.org/10.1007/s11579-024-00358-y","url":null,"abstract":"<p>The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the optimal solution using a terminal perturbation method and properties of Bounded Mean Oscillation (BMO) martingales. The necessary condition is further proved to be sufficient for the existence of an optimal solution under an additional convexity assumption. Finally, the optimality condition is applied to discuss problems of partial hedging with ambiguity, fundraising under ambiguity and randomized testing problems for a quadratic <i>g</i>-expectation.\u0000</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"8 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154207","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
Robust non-zero-sum stochastic differential game of two insurers with common shock and CDS transaction 具有共同冲击和 CDS 交易的两家保险公司的稳健非零和随机微分博弈
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-03-18 DOI: 10.1007/s11579-024-00357-z
Man Li, Ying Huang, Ya Huang, Jieming Zhou
{"title":"Robust non-zero-sum stochastic differential game of two insurers with common shock and CDS transaction","authors":"Man Li, Ying Huang, Ya Huang, Jieming Zhou","doi":"10.1007/s11579-024-00357-z","DOIUrl":"https://doi.org/10.1007/s11579-024-00357-z","url":null,"abstract":"<p>This paper considers the non-zero-sum stochastic differential game problem between two ambiguity-averse insurers (AAIs) with common shock. Each AAI’s surplus process consists of a proportional reinsurance protection and an investment in a money account, a stock and a credit default swap (CDS) with the objective of maximizing the expected utility of her relative terminal surplus with respect to that of her competitors. We consider default contagion risk of CDSs through a Markovian model with interacting default intensities. It is worthwhile to consider the uncertainty of the model on both the insurer herself and her competitors. In our model, we describe the surplus processes of two insurers by two jump-diffusion models with a common shock. Under jump-diffusion models, the robust Nash equilibrium strategies and the value functions for the all-default, one-default and all-alive case are derived under a worst-case scenario, respectively. Finally, through some numerical examples, we found some interesting results about the effects of some model parameters on the robust Nash equilibrium strategies, such as, the common shocks and the individual claims have the opposite effect on reinsurance investment.\u0000</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"15 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154175","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
Nash equilibria for relative investors with (non)linear price impact 具有（非）线性价格影响的相对投资者的纳什均衡
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-02-28 DOI: 10.1007/s11579-024-00356-0
Nicole Bäuerle, Tamara Göll
{"title":"Nash equilibria for relative investors with (non)linear price impact","authors":"Nicole Bäuerle, Tamara Göll","doi":"10.1007/s11579-024-00356-0","DOIUrl":"https://doi.org/10.1007/s11579-024-00356-0","url":null,"abstract":"<p>We consider the strategic interaction of <i>n</i> investors who are able to influence a stock price process and at the same time measure their utilities relative to the other investors. Our main aim is to find Nash equilibrium investment strategies in this setting in a financial market driven by a Brownian motion and investigate the influence the price impact has on the equilibrium. We consider both CRRA and CARA utility functions. Our findings show that the problem is well-posed as long as the price impact is at most linear. Moreover, numerical results reveal that the investors behave very aggressively when the price impact is close to a critical parameter.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"13 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140002649","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
Modelling the industrial production of electric and gas utilities through the $$CIR^3$$ model 通过 CIR^3$$ 模型模拟电力和天然气公司的工业生产
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-02-10 DOI: 10.1007/s11579-023-00350-y
Claudia Ceci, Michele Bufalo, Giuseppe Orlando
{"title":"Modelling the industrial production of electric and gas utilities through the $$CIR^3$$ model","authors":"Claudia Ceci, Michele Bufalo, Giuseppe Orlando","doi":"10.1007/s11579-023-00350-y","DOIUrl":"https://doi.org/10.1007/s11579-023-00350-y","url":null,"abstract":"<p>This work aims to extend previous research on how a trifactorial stochastic model, which we call <span>(CIR^3)</span>, can be turned into a forecasting tool for energy time series. In particular, in this work, we intend to predict changes in the industrial production of electric and gas utilities. The model accounts for several stylized facts such as the mean reversion of both the process and its volatility to a short-run mean, non-normality, autocorrelation, cluster volatility and fat tails. In addition to that, we provide two theoretical results which are of particular importance in modelling and simulations. The first is the proof of existence and uniqueness of the solution to the SDEs system that describes the model. The second theoretical result is to convert, by the means of Lamperti transformations, the correlated system into an uncorrelated one. The forecasting performance is tested against an ARIMA-GARCH and a nonlinear regression model (NRM).</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"7 4 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139761946","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
Countercyclical unemployment benefits: a general equilibrium analysis of transition dynamics 反周期失业福利：过渡动态的一般均衡分析
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-02-01 DOI: 10.1007/s11579-023-00351-x
Erhan Bayraktar, Indrajit Mitra, Jingjie Zhang
{"title":"Countercyclical unemployment benefits: a general equilibrium analysis of transition dynamics","authors":"Erhan Bayraktar, Indrajit Mitra, Jingjie Zhang","doi":"10.1007/s11579-023-00351-x","DOIUrl":"https://doi.org/10.1007/s11579-023-00351-x","url":null,"abstract":"<p>We analyze the general equilibrium effects of countercyclical unemployment benefit policies. Our heterogenous-agent model features costly job search with imperfect insurance of unemployment risk and individual savings. Our model predicts: (1) the additional unemployment under a countercyclical policy relative to that under an acyclical policy to be a superlinear function of the aggregate shock?s size, (2) a higher unemployment rate sensitivity to UI policy changes when individual savings are relatively low. Our estimates of the effects of UI policy changes are based on transition dynamics following a large, unanticipated increase in the unemployment rate.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"180 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139664184","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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