TIME INCONSISTENCY AND REPUTATION IN MONETARY POLICY: A STRATEGIC MODELLING IN CONTINUOUS TIME

This article develops a model to examine the equilibrium behavior of the time inconsistency problem in a continuous time economy with stochastic and endogenized dis-tortion. First, the authors introduce the notion of sequentially rational equilibrium, and show that the time inconsistency problem may be solved with trigger reputation strategies for stochastic setting. The conditions for the existence of sequentially rational equilibrium are provided. Then, the concept of sequentially rational stochastically stable equilibrium is introduced. The authors compare the relative stability between the cooperative behavior and uncooperative behavior, and show that the cooperative equilibrium in this monetary policy game is a sequentially rational stochastically stable equilibrium and the uncooper-ative equilibrium is sequentially rational stochastically unstable equilibrium. In the long run, the zero inflation monetary policies are inherently more stable than the discretion rules, and once established, they tend to persist for longer periods of the time.     

Tracking error decision rules and accumulated wealth

There is compelling evidence that typical decision‐makers, including individual investors and even professional money managers, care about the difference between their portfolio returns and a reference point, or benchmark return. In the context of financial markets, likely benchmarks against which investors compare their own returns include easy‐to‐focus‐on numbers such as one's own past payoffs, historical average payoffs, and the payoffs of competitors. Referring to the gap between one's current portfolio return and the benchmark return as ‘tracking error’, this paper develops a simple model to study the consequences and possible origins of investors who use expected tracking error to guide their portfolio decisions, referred to as ‘tracking error types’. In particular, this paper analyses the level of risk‐taking and accumulated wealth of tracking error types using standard mean‐variance investors as a comparison group. The behaviour of these two types are studied first in isolation, and then in an equilibrium model. Simple analytic results together with statistics summarizing simulated wealth accumulations point to the conclusion that tracking error—whether it is interpreted as reflecting inertia, habituation, or a propensity to make social comparisons in evaluating one's own performance—leads to greater risk‐taking and greater shares of accumulated wealth. This result holds even though the two types are calibrated to be identically risk‐averse when expected tracking error equals zero. In the equilibrium model, increased aggregate levels of risk‐taking reduce the returns on risk. Therefore, the net social effect of tracking‐error‐induced risk‐taking is potentially ambiguous. This paper shows, however, that tracking error promotes a pattern of specialization that helps the economy move towards the path of maximum accumulated wealth.     

The equity risk premium and the riskfree rate in an economy with borrowing constraints

Our objective is to study analytically the effect of borrowing constraints on asset returns. We explicitly characterize the equilibrium for an exchange economy with two agents who differ in their risk aversion and are prohibited from borrowing. In a representative-agent economy with CRRA preferences, the Sharpe ratio of equity returns and the riskfree rate are linked by the risk aversion parameter. We show that allowing for preference heterogeneity and imposing borrowing constraints breaks this link. We find that an economy with borrowing constraints exhibits simultaneously a relatively high Sharpe ratio of stock returns and a relatively low riskfree interest rate, compared to both representative-agent and unconstrained heterogeneous-agent economies.      

均衡的再保险市场

本文讨论了再保险市场达到均衡状态的定义、性质以及与 Pareto最优的关系 .     

带风险指数的金融均衡的存在性定理及其结构特征（上）

本文主要论证了在不完全市场条件下带风险指数的金融均衡的存在性，并揭示其均衡结构的特征．本文中建立的模型是一、二期货币投入产出金融经济且具有可微的资产结构，这一模型包括了许多具有特殊资产结构的均衡模型，如实资产结构、应资产结构、恒秩资产结构的均衡模型．因此本文的这一模型具有广泛的应用前景和实用价值．接着给出了本文的金融均衡的存在性定理，再借助微分拓扑给出它的证明过程，这一证明过程较之以前证明均衡存在性的经典方法（如Ｄｕｆｆｉｅ，Ｄ＆Ｗ．Ｓｈｆｅｒ（１９８５）的方法）要简便得多．同时也应注意到本文的这一结论既适用于资产市场下含随机风险因素的情形，也适用于商品空间为无限维的情形．除此之外，还给出了怎样判别资产结构是否属于Ｔ类的判别法，为检验均衡存在性提供了更为便利的途径．最后，本文论证了在金融市场里，尽管由于稀缺性的存在，从而导致均衡分配的多样化，然而均衡分配集却形成了一光滑子流，但该流形的维数与稀缺性有关．换句话说，尽管市场是不完全的，但均衡分配不确定性的度却是可比的．如此使得人们对均衡资产结构的认识更进一步．     

The behavior of individual and aggregate stock prices

News about an individual stock normally has only a trivial impact on the aggregate economy. The news of the aggregate stock market, however, may have a significant impact on the prospects of the economy, and so has a large impact on the pricing kernel. This difference between the aggregate stock market and individual stocks is analyzed in a dynamic general equilibrium setting with incomplete information. The main findings are as follows. First, consistent with existing empirical evidence, the correlation between stock returns and earnings surprises is, on average, positive at the individual stock level and is lower or even negative at the aggregate level. Second, a stock’s return is less sensitive to its earnings surprises if the expected earnings growth of the stock is more pro-cyclical. Third, a decrease of information quality of a stock increases its risk premium if the stock accounts for a small fraction of the economy, but decreases its risk premium if the stock accounts for a large fraction.     

考虑损失厌恶行为与谈判破裂的Rubinstein谈判博弈研究

本文考虑具有损失厌恶行为与破裂风险的Rubinstein谈判博弈。首先构建子博弈完美均衡,并证明子博弈完美均衡的存在性及唯一性。然后分析子博弈完美均衡的性质,结果表明:参与人受益于对手的损失厌恶行为,而因自身具有损失厌恶行为遭受损失;谈判破裂概率对均衡结果的影响取决于贴现因子与参与人的损失厌恶系数;当谈判破裂的概率趋于零时,极限均衡结果收敛于经典的Rubinstein谈判博弈结果。最后建立了与非对称Nash谈判解的关系,其中参与人的议价能力与自身的损失厌恶水平呈负相关性,与对手的损失厌恶水平呈正相关性;参与人的议价能力依赖于谈判破裂概率与出价时间间隔的比值。     

保险中遏制投保人逆向选择的博弈策略分析

以投保人的风险类型难于鉴别的逆向选择问题为研究对象,建立了投保人与保险公司的双人非零和博弈模型,并求解得出了该博弈的混合策略纳什均衡点,从而得出重罚有利于遏制投保人的逆向选择以及使保险公司的期望利润为零的保险定价公式.     

无套利期权定价模型在一般均衡框架下的一致性研究

期权定价有无套利方法和一般均衡方法两种.本文在一般均衡框架下构造了一个允许连续消费的简单经济模型,并将基于无套利方法的期权定价模型中所假定的标的证券的价格变化动态过程内生化于理性预期均衡中.在常数相对风险厌恶(CRRA)的效用函数的条件下,我们推导出Merton(1973)期权定价公式,从而证明无套利方法与均衡方法的内在一致性,而CRRA这种类型的效用函数是无套利定价模型在一般均衡框架中成立的充分条件.本文进一步将此模型在一个简单经济中扩展到m种证券的情况,也得到相似的结论.     

Multiple Priors and Asset Pricing

The asset pricing implications of a statistical model consistent with multiple priors, or beliefs about return distributions, are developed. It is shown that quite generally equilibrium differences in mean returns across priors are to be explained in terms of perceived risk differences between these priors. Advances in filtering theory are employed on time series data to filter all the multiple state conditional components of risks and rewards. It is then observed that excess return differentials across priors are broadly consistent with required risk compensations under these priors, though the sharp hypothesis of zero intercept and unit slope is rejected. The filtered results also deliver numerous other interesting statistics. Here we focus on the construction of long horizon return distributions from data on daily returns using a Markov chain approach to incorporate stochasticity in elementary risk characterizations like volatility, skewness and kurtosis.      

Endogenous Fluctuations in Two-Sector Models: Role of Preferences

We consider a discrete-time two-sector CES (constant elasticity of substitution) economy with sector specific external effects and nonlinear preferences. Our goal is to examine carefully the influence of the utility curvature on the occurrence of multiple equilibria. We show that local indeterminacy depends on an interplay between factor substitutability and the elasticity of intertemporal substitution in consumption. Moreover, considering that, when the external effects are set equal to zero, we get a two-sector optimal growth model, we study also the role of the utility curvature on the occurrence of competitive equilibrium cycles. We show that persistent endogenous fluctuations and macroeconomic volatility require a strong enough elasticity of intertemporal substitution in consumption. We thank two anonymous referees for helpful comments and suggestions. External effects are feedbacks from the other agents in the economy who face also identical maximizing problems. See Benhabib and Farmer (Ref. 1) for a survey. Global indeterminacy based on a finite number of equilibria is associated with the existence of thresholds and multiple steady states. See Deissenberg, Feichtinger, Semmler, and Wirl (Ref. 2).     

Zero‐Hopf bifurcation in the Volterra‐Gause system of predator‐prey type

We prove that the Volterra‐Gause system of predator‐prey type exhibits 2 kinds of zero‐Hopf bifurcations for convenient values of their parameters. In the first, 1 periodic solution bifurcates from a zero‐Hopf equilibrium, and in the second, 4 periodic solutions bifurcate from another zero‐Hopf equilibrium. This study is done using the averaging theory of second order.     

Walrasian foundations for equilibria in segmented markets

We study a CAPM economy with segmented financial markets and competitive arbitrageurs who link these markets. We show that the equilibrium of the arbitraged economy is Walrasian in the sense that it coincides with the equilibrium of an appropriately defined competitive economy with no arbitrageurs. This characterization serves to clarify the role that arbitrageurs play in integrating markets.     

A smooth path-following algorithm for market equilibrium under a class of piecewise-smooth concave utilities

This paper presents a smooth path-following algorithm for computing market equilibrium in a pure exchange economy under a class of piecewise-smooth concave utilities, which can be expressed as \(u(x)=\min _\ell \{f_\ell (x)\}\) with \(f_\ell (x)\) being a smooth concave function for all \(\ell \). As a result of a smooth technique for minimax problems, a smooth homotopy mapping is derived from the introduction of logarithmic barrier terms and an extra variable. With this mapping, it is proved that there always exists a smooth path leading to a market equilibrium as the extra variable approaches zero. A predictor–corrector method is adapted for numerically following this path. Numerical results are given to further demonstrate the effectiveness and efficiency of the algorithm.     

Zero relaxation and dissipation limits for hyperbolic conservation laws

We are interested in hyperbolic systems of conservation laws with relaxation and dissipation, particularly the zero relaxation limit. Such a limit is of interest in several physical situations, including gas flow near thermo-equilibrium, kinetic theory with small mean free path, and viscoelasticity with vanishing memory. In this article we study hyperbolic systems of two conservation laws with relaxation. For the stable case where the equilibrium speed is subcharacteristic with respect to the frozen speeds, we illustrate for a model in viscoelasticity that no oscillation develops for the nonlinear system in the zero relaxation limit. For the marginally stable case where the equilibrium speed may equal one of the frozen speeds, we show for a model in phase transitions that no oscillation arises when the dissipation is present and goes to zero more slowly than the relaxation. Our analysis includes the construction of suitable entropy pairs to derive energy estimates. We need such energy estimates not only for the compactness properties but also for the deviation from the equilibrium of the solutions for the relaxation systems. The theory of compensated compactness is then applied to study the oscillation in the zero relaxation limit. © 1993 John Wiley & Sons, Inc.     

Financial networks with intermediation: Risk management with variable weights

In this paper, we develop a framework for the modeling, analysis, and computation of solutions to multitiered financial network problems with intermediaries in which both the sources of financial funds as well as the intermediaries are multicriteria decision-makers. In particular, we assume that these decision-makers seek not only to maximize their net revenues but also to minimize risk with the risk being penalized by a variable weight. We make explicit the behavior of the various decision-makers, including the consumers at the demand markets for the financial products. We derive the optimality conditions, and demonstrate that the governing equilibrium conditions of the financial network economy can be formulated as a finite-dimensional variational inequality problem. Qualitative properties of the equilibrium financial flow and price pattern are provided. A computational procedure that exploits the network structure of the problem is proposed and then applied to several numerical examples.     

离散无穷时期不完全资产市场随机平衡

Abstract. This paper examines the existence of general equilibrium in a discrete time economywith the infinite horizon incomplete markets. There is a single good at each node in the eventtree. The existence of general equilibrium for the infinite horizon economy is proved by takinglimit of equilibria in truncated economies in which trade stops at a sequence of dates.     

Rational ignorance and voting behavior

We model a two-alternative election in which voters may acquire information about which is the best alternative for all voters. Voters differ in their cost of acquiring information. We show that as the number of voters increases, the fraction of voters who acquire information declines to zero. However, if the support of the cost distribution is not bounded away from zero, there is an equilibrium with some information acquisition for arbitrarily large electorates. This equilibrium dominates in terms of welfare any equilibrium without information acquisition – even though generally there is too little information acquisition with respect to an optimal strategy profile.      

Demand for longevity securities under relative performance concerns: Stochastic differential games with cointegration

This paper investigates the impact of relative performance concerns on the longevity risk transfer market. When an insurer concerns about the relative performance in a two-insurer economy, she maximizes the expected utility of her terminal wealth benchmarked against her competitor’s. The problem formulation for a general utility, a general interest rate process and cointegrated mortality rates uses a nonzero sum stochastic differential game approach. Explicit solution of the Nash equilibrium is derived for constant relative risk adverse insurers under the Vasicek-type stochastic interest and mortality rates. Existence and uniqueness of the Nash equilibrium are established for the CIR-type models, which rule out negative interest and mortality rates. While previous studies based on the single-agent approaches have shown a high investment demand in longevity bonds, the launch of it was unsuccessful in reality. Ours supplements that the demand is much lower subject to the relative performance concerns.     

Financial networks with socially responsible investing

In this paper, we develop a framework for the modeling, analysis, and computation of solutions to multitiered financial network problems with socially responsible investment in which both the sources of financial funds as well as the intermediaries are multicriteria decision-makers. We assume that these decision-makers seek not only to maximize their net revenues but also minimize risk with the risk being penalized by a variable weight. Furthermore, we assume that the intermediaries are socially responsible companies, who want to maximize their social responsibility levels. We make explicit the behavior of the various decision-makers, including the consumers at the demand markets for the financial products. We derive the optimality conditions, and demonstrate that the governing equilibrium conditions of the financial network economy can be formulated as a finite-dimensional variational inequality problem. Qualitative properties of the equilibrium financial flow and price pattern are provided. A numerical example is used to illustrate the model.