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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 Q3 BUSINESS, FINANCE Pub Date : 2024-05-02 DOI: 10.1007/s11579-024-00360-4
Zongxia Liang, Keyu Zhang

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 n-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 n agents, an approximate Nash equilibrium is then constructed using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained. In addition, we provide some numerical illustrations of our results.

本文研究的是具有指数效用或幂效用以及共同有限时间跨度的竞争代理的最优投资-消费问题。每个代理都将所有同行的习惯养成和财富的平均值视为评估其决策绩效的基准。我们提出了两种效用下的 n 个代理博弈问题和相应的均值场博弈问题。每个问题都有一个均值场均衡。在每个有 n 个代理的问题中,当 n 足够大时,利用得到的均值场均衡构建近似纳什均衡。每个问题的收敛阶数也可以明确得到。此外,我们还提供了一些结果的数值说明。
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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 Q3 BUSINESS, FINANCE Pub Date : 2024-03-27 DOI: 10.1007/s11579-024-00353-3
Ludovic Tangpi, Shichun Wang

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 entry threshold 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.

在本文中,我们进一步扩展了 Tangpi 和 Wang(Optimal bubble riding: a mean field game with varying entry times, 2022)中提出的最优乘泡沫模型,允许价格依赖的进入时间。代理的特征是他们各自的进入门槛,这代表了他们对泡沫强度的信念。反之,泡沫的增长动力来自参与者的涌入。依赖价格的进入自然会导致具有共同噪声和随机进入时间的均值控制博弈,我们为此提供了一个存在性结果。我们首先求解弱式博弈的离散化版本,然后检验其极限可测性,从而得到均衡。在本文中,共同噪声有两个来源:所有代理人交易的资产价格和外生泡沫破裂时间。
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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 Q3 BUSINESS, FINANCE Pub Date : 2024-03-26 DOI: 10.1007/s11579-024-00354-2
S. Ankirchner, N. Kazi-Tani, J. Wendt, C. Zhou

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 ([sigma _1, sigma _2]), 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 (p in (0,1)) 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 n-fold tuple of this threshold strategy is an approximate Nash equilibrium of the n-player game. Finally, we show that the more time a player has at her disposal, the higher her chances of winning.

我们考虑的是一个随机微分博弈,其中每个博弈者都持续控制着自己状态过程的扩散强度。博弈者都必须从相同的扩散率区间 ([sigma _1,sigma _2])中选择,并且各自的随机时间跨度都是从相同的分布中独立抽取的。玩家在各自的时间跨度上的状态是所有终端状态中最好的(p in (0,1)),那么他们就会得到固定的奖金。我们证明,在该博弈的均值场版本中存在一个均衡,即当状态低于给定阈值时,代表博弈者选择最大的扩散率,而在其他情况下则选择最小的扩散率。这种阈值策略的对称 n 倍元组是 n 人博弈的近似纳什均衡。最后,我们证明,玩家可支配的时间越多,获胜的几率就越大。
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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 Q3 BUSINESS, FINANCE Pub Date : 2024-03-21 DOI: 10.1007/s11579-024-00359-x
Andrea Modena, Luca Regis

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.

我们建立了一个动态经济模型,在该模型中,自营职业企业家将其净资产分配给公司资本和无风险政府债券,同时面临借贷限制、不可保险的劳动力禀赋和资本折旧风险。我们推导出模型均衡的数值近似值,并将其与无资本风险的基准经济进行比较。与劳动力禀赋风险不同,资本风险会减少总资本积累和工资,并产生正的风险溢价。低(高)净值企业家的消费主要依赖于劳动(金融)收入,他们持有较高(较低)的资本风险。这些模式加剧了不平等,增加了财务受限个人的比例,并使净值分布的尾部更加肥胖。财政政策通过重新分配资源和影响风险溢价来影响这些结果。资本税的削减会使更多的低净值或高净值企业家受益,这取决于是对债券征税还是对劳动收入征税。
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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 Q3 BUSINESS, FINANCE Pub Date : 2024-03-18 DOI: 10.1007/s11579-024-00355-1
Delia Coculescu, Médéric Motte, Huyên Pham

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.

我们研究的是一个大群体中的二元意见形成,在这个群体中,个体会受到其他个体意见的影响。该群体的特点是:(i) 存在个体具有某些相似特征的社群;(ii) 可能在短期内引发不可预测的意见转变的意见领袖;(iii) 在观察个体或公众意见过程时存在一定程度的不完全信息。在这种情况下,我们研究了三种不同的近似机制:普通抽样近似、独立抽样近似以及本文的重点--麦肯-弗拉索夫(或均值场)近似。我们的研究表明,所有这三种近似方法在我们引入的用于衡量群体水平和个体水平误差的不同指标方面都表现出色。在存在以主要影响因素意见过程为代表的共同噪声的情况下,尽管不存在特异性噪声,我们还是得出了混沌传播类型的结果。对于线性模型的特殊情况和主要影响者舆论动态的特殊规格,我们提供了额外的分析,包括舆论的长期行为和波动。一些具体实例和数值分析对理论结果进行了补充,说明了回声室的形成、混沌传播以及雪球效应和社会惯性等现象。
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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 Q3 BUSINESS, FINANCE Pub Date : 2024-03-18 DOI: 10.1007/s11579-024-00358-y
Peng Luo, Alexander Schied, Xiaole Xue

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 g-expectation.

本文研究的是一种带约束条件的鲁棒优化问题。该问题是通过具有二次生成器的后向随机微分方程(BSDE)提出的。利用终端扰动方法和有界均值振荡(BMO)马氏体的特性,为最优解建立了必要条件。在额外的凸性假设下,必要条件进一步证明了最优解存在的充分性。最后,最优条件被应用于讨论具有模糊性的部分对冲问题、模糊性下的筹款问题以及二次 g 期望的随机测试问题。
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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 Q3 BUSINESS, FINANCE Pub Date : 2024-03-18 DOI: 10.1007/s11579-024-00357-z
Man Li, Ying Huang, Ya Huang, Jieming Zhou

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.

本文考虑了两个具有共同冲击的模糊规避型保险公司(AAI)之间的非零和随机差分博弈问题。每个 AAI 的盈余过程都由按比例的再保险保障以及对货币账户、股票和信用违约掉期(CDS)的投资组成,目标是最大化其相对于竞争对手的相对最终盈余的预期效用。我们通过一个违约强度相互影响的马尔可夫模型来考虑 CDS 的违约传染风险。值得考虑的是该模型对保险人本身及其竞争对手的不确定性。在我们的模型中,我们通过两个具有共同冲击的跳跃-扩散模型来描述两个保险公司的盈余过程。在跳跃扩散模型下,我们分别推导出了在最坏情况下全部违约、一次违约和全部生存情况下的稳健纳什均衡策略和价值函数。最后,通过一些数值示例,我们发现了一些模型参数对稳健纳什均衡策略影响的有趣结果,如共同冲击和个别索赔对再保险投资的影响是相反的。
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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 Q3 BUSINESS, FINANCE Pub Date : 2024-02-28 DOI: 10.1007/s11579-024-00356-0
Nicole Bäuerle, Tamara Göll

We consider the strategic interaction of n 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.

我们考虑的是 n 个投资者的战略互动,他们能够影响股票价格进程,同时衡量自己相对于其他投资者的效用。我们的主要目的是在由布朗运动驱动的金融市场中找到纳什均衡投资策略,并研究价格影响对均衡的影响。我们同时考虑了 CRRA 和 CARA 效用函数。我们的研究结果表明,只要价格影响至多是线性的,问题就能得到很好的解决。此外,数值结果显示,当价格影响接近临界参数时,投资者的行为非常激进。
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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 Q3 BUSINESS, FINANCE Pub Date : 2024-02-10 DOI: 10.1007/s11579-023-00350-y
Claudia Ceci, Michele Bufalo, Giuseppe Orlando

This work aims to extend previous research on how a trifactorial stochastic model, which we call (CIR^3), 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).

这项工作旨在扩展之前的研究,探讨如何将我们称之为 (CIR^3)的三因素随机模型转化为能源时间序列的预测工具。特别是,在这项工作中,我们打算预测电力和天然气公用事业的工业生产变化。该模型考虑了几个典型事实,如过程及其波动的均值回归到短期均值、非正态性、自相关性、群集波动性和肥尾。除此之外,我们还提供了两个对建模和模拟特别重要的理论结果。第一个是证明了描述模型的 SDE 系统解的存在性和唯一性。第二个理论结果是通过兰佩蒂变换将相关系统转换为非相关系统。预测性能对照 ARIMA-GARCH 模型和非线性回归模型(NRM)进行了测试。
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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 Q3 BUSINESS, FINANCE Pub Date : 2024-02-01 DOI: 10.1007/s11579-023-00351-x
Erhan Bayraktar, Indrajit Mitra, Jingjie Zhang

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.

我们分析了反周期失业福利政策的一般均衡效应。我们的异质代理模型具有高成本求职、不完全失业风险保险和个人储蓄的特点。我们的模型预测:(1) 相对于非周期性政策,反周期政策下的额外失业率是总体冲击大小的超线性函数;(2) 当个人储蓄相对较低时,失业率对失业保险政策变化的敏感性更高。我们对失业保险政策变化影响的估计是基于失业率大幅、意外上升后的过渡动态。
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引用次数: 0
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Mathematics and Financial Economics
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