Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty

In diffusion models, a few suitably chosen financial securities allow to complete the market. As a consequence, the efficient allocations of static Arrow–Debreu equilibria can be attained in Radner equilibria by dynamic trading. We show that this celebrated result generically fails if there is Knightian uncertainty about volatility. A Radner equilibrium with the same efficient allocation as in an Arrow–Debreu equilibrium exists if and only if the discounted net trades of the equilibrium allocation display no ambiguity in the mean. This property is violated generically in endowments, and thus Arrow–Debreu equilibrium allocations are generically unattainable by dynamically trading a few long-lived assets.     

Financial Markets for Unknown Risks if Beliefs Differ

We consider a general equilibrium model with individual and collective risks. The article builds on a contribution by Chichilnisky and Heal, who show that contingent Arrow–Debreu equilibria can also be supported in economies with Arrow securities and mutual insurance contracts. However, they show this to be true in general only if beliefs are identical, a very restrictive assumption in the context of unknown risks. Moreover, they claim complete insurance in equilibrium to be impossible if beliefs are different. We show that even with different beliefs, firstly, complete insurance is possible in each statistical state, and secondly, contingent equilibrium can still be supported in economies with insurance and securities.     

Financial equilibrium with non-linear valuations

Classical Arrow Debreu equilibria employ budget feasibility to require individuals to ensure excess supplies to be nonnegative in value using the single equilibrium price system for valuation purposes. Yet by the selection of state contingent prices, they seek excess supplies that are nonnegative in each component, and not just the value. A financial equilibrium, on the other hand, defines acceptable economic risks as excess supplies that are nonnegative in value for a number of prespecified valuation price systems. The collection of prespecified valuation price systems may be referred to as features for which clearing is sought. The number of features will generally be less than the number of states. It is then shown that by also defining budget feasibility nonlinearly one may construct a financial equilibrium with fewer securities than there are features to be cleared.     

Competitive risk sharing contracts with one-sided commitment

This paper analyzes dynamic equilibrium risk sharing contracts between profit-maximizing intermediaries and a large pool of ex ante identical agents that face idiosyncratic income uncertainty that makes them heterogeneous ex post. In any given period, after having observed her income, the agent can walk away from the contract, while the intermediary cannot, i.e. there is one-sided commitment. We consider the extreme scenario that the agents face no costs to walking away, and can sign up with any competing intermediary without any reputational losses. We demonstrate that not only autarky, but also partial and full insurance can obtain, depending on the relative patience of agents and financial intermediaries. Insurance can be provided because in an equilibrium contract an up-front payment effectively locks in the agent with an intermediary. We then show that our contract economy is equivalent to a consumption-savings economy with one-period Arrow securities and a short-sale constraint, similar to Bulow and Rogoff [1989. Sovereign debt: is to forgive to forget? American Economic Review 79, 43-50]. From this equivalence and our characterization of dynamic contracts it immediately follows that without cost of switching financial intermediaries debt contracts are not sustainable, even though a risk allocation superior to autarky can be achieved.     

证券市场监管者和中小投资者博弈分析

由于我国证券市场发展尚未成熟,同时因为我国的特殊经济模式,监管在维护证券市场稳定发展方面起了很重要的作用。但是,由于我国监管体系的不完善,信息的不透明和不对称性会产生投机行为,中小投资者往往就成为股市博弈的牺牲品。因此,本文将通过对市场过热和市场低迷两种情况下,监管者颁布政策和中小投资者投资行为之间的博弈过程进行分析,以求规范股市投机行为,维护各方利益均衡,达到市场稳定发展。本文的分析表明监管者和中小投资者的均衡策略主要取决于其得到的效用和付出的成本,在不同的临界值下存在不同的均衡结果。最后针对本文的结论和我国的实际情况,提出了相应的建议。     

Equilibrium returns with transaction costs

We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean–variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique solution of a system of coupled but linear forward–backward stochastic differential equations. Explicit solutions are obtained in a number of concrete settings. The sluggishness of the frictional portfolios makes the corresponding equilibrium returns mean-reverting. Compared to the frictionless case, expected returns are higher if the more risk-averse agents are net sellers or if the asset supply expands over time.     

Bear beta

We test whether bear market risk, time variation in the probability of future bear market states, is priced. We construct an Arrow–Debreu security that pays off in bear market states (AD Bear) from traded Standard & Poor’s (S&P) 500 index options and use its returns to measure bear market risk. We find that bear beta (exposure to bear market risk) has a strong relation with expected stock returns that is robust, persistent, and remains strong among liquid and large stocks. Historical bear beta also predicts future bear market risk exposure. We conclude that bear market risk is priced in the cross section of stock returns.     

Self-enforcing employment contracts and business cycle fluctuations

This paper incorporates risk-sharing employment contracts into an economy in which matching frictions characterize the labour market and in which agents cannot commit. In equilibrium, the terms of ongoing contracts are affected by those being negotiated in the job market because contracts must be self-enforcing. In this context, risk-sharing implies that hours worked and wages are negatively related, while enforcement considerations imply the converse. Overall, the sign of this relationship is ambiguous. Therefore, the existence of such contracts may explain why movements in hours worked appear weakly related to those in real wages in U.S. aggregate data.     

Heterogeneous preferences and equilibrium trading volume

The representative-agent Lucas model stresses aggregate risk and hence does not allow us to study the impact of agents’ heterogeneity on the dynamics of equilibrium trading volume. In this paper, we investigate under what conditions non-informational heterogeneity, i.e., differences in preferences and endowments, leads to nontrivial trading volume in equilibrium. We present a non-informational no-trade theorem that provides necessary and sufficient conditions for zero equilibrium trading volume in a continuous-time Lucas market model with heterogeneous agents, multiple goods, and multiple securities. We explain in detail how no-trade equilibria are related to autarky equilibria, portfolio autarky equilibria, and peculiar financial market equilibria, which play an important role in the literature on international risk sharing.     

Competitive equilibrium with type convergence in an asymmetrically informed market

This article studies an asymmetric information game with 'typeconvergence', in which, under some realizations of a commonuncertainty, inducing informed agents to reveal their typesthrough self-selection by contract choice is either costly orimpossible. Under other realizations, self-selection permitscostless distinctions between informed agents. I obtain sufficientconditions under which contracting with options prior to therealization of the common uncertainty leads to the existenceof a perfectly separating, costless Nash equilibrium. Applicationsto variable rate loan commitments and life insurance contractingare discussed.     

Equilibrium Pricing of General Insurance Policies

Abstract

A model is developed for determining the price of general insurance policies in a competitive, noncooperative market. This model extends previous single-optimizer pricing models by supposing that each participant chooses an optimal pricing strategy. Specifically, prices are determined by finding a Nash equilibrium of an N-player differential game. In the game, a demand law describes the relationship between policy sales and premium, and each insurer aims to maximize its (expected) utility of wealth at the end of the planning horizon. Two features of the model are investigated in detail: the effect of limited total demand for policies, and the uncertainty in the calculation of the breakeven (or cost price) of an insurance policy.

It is found that if the demand for policies is unlimited, then the equilibrium pricing strategy is identical for all insurers, and it can be found analytically for particular model parameterizations. However, if the demand for policies is limited, then, for entrants to a new line of business, there are additional asymmetric Nash equilibria with insurers alternating between maximal and minimal selling. Consequently it is proposed that the actuarial cycle is a result of price competition, limited demand, and entry of new insurers into the market. If the breakeven premium is highly volatile, then the symmetric equilibrium premium loading tends to a constant, and it is suggested that this will dampen the oscillatory pricing of new entrants.     

合谋操纵与散户跟风的演化博弈分析

本文通过构造一个合谋操纵和散户跟风的双种群双策略的演化博弈模型,从规范经济学角度研究了合谋账户与散户之间的演化博弈,分析了合谋操纵者何时会选择操纵、散户是否会跟风、监管对市场操纵的影响以及市场环境如何影响合谋操纵者和散户的行为等问题。为追求利益最大化,拥有资金优势的合谋者具有操纵市场的动机;合谋者操纵市场行为损害了一些跟风散户的利益,一定程度上也会减少散户跟风。基于此,本文认为,应当通过完善法制,保持监管高压态势,加强投资者教育和投资者适当性管理,完善套利制度等,应对合谋操纵和散户跟风行为。     

A financial CCAPM and economic inequalities

This paper considers a wealth heterogeneous multi-agent (MA) financial pricing CCAPM model. It is based on the following observations: (a) A distinction between what agents are willing to pay for consumption and what they actually pay. The former is a function of a number of factors including the agent’s wealth and risk preferences and the latter is a function of all other agents’ aggregate consumption or equivalently, their wealth committed to consumption. (b) Unlike traditional pricing models that define a representative agent underlying the pricing model, this paper assumes that each agent is in fact ‘Cournot-gaming’ a market defined by all other agents. This results in a decomposition of an n-agents game into n games of two agents, one a specific agent and the other a synthetic agent (a proxy for all other agents), on the basis of which an equilibrium consumption price solution is defined. The paper’s essential results are twofold. First, a Martingale pricing model is defined for each individual agent expressing the consumer willingness to pay (his utility price) and the market price—the price that all agents pay for consumption. In this sense, price is unique defined by each agent’s ‘Cournot game’ Agents’ consumption are then adjusted accordingly to meet the market price. Second, the pricing model defined is shown to account for agents wealth distribution pointing out that all agents valuations are a function of their and others’ wealth, the information they have about each other and other factors which are discussed in the text. When an agent has no wealth or cannot affect the market price of consumption, then this pricing model is reduced to the standard CCAPM model while any agent with an appreciable wealth compared to other agents, is shown to value returns (and thus future consumption) less than wealth-poor agents. As a result, this paper will argue that even in a financial market with an infinite number of agents, if there are some agents that are large enough to affect the market price by their decisions, such agents have an arbitrage advantage over the poorer agents. The financial CCAPM MA pricing model has a number of implications, some of which are considered in this paper. Finally, some simple examples are considered to highlight the applicability of this paper to specific financial issues.     

Stability of Radner equilibria with respect to small frictions

We study risk-sharing equilibria with trading subject to small proportional transaction costs. We show that the frictionless equilibrium prices also form an “asymptotic equilibrium” in the small-cost limit. More precisely, there exist asymptotically optimal policies for all agents and a split of the trading cost according to their risk aversions for which the frictionless equilibrium prices still clear the market. Starting from a frictionless equilibrium, this allows studying the interplay of volatility, liquidity and trading volume.     

A time-inconsistent Dynkin game: from intra-personal to inter-personal equilibria

This paper studies a nonzero-sum Dynkin game in discrete time under non-exponential discounting. For both players, there are two intertwined levels of game-theoretic reasoning. First, each player looks for an intra-personal equilibrium among her current and future selves, so as to resolve time inconsistency triggered by non-exponential discounting. Next, given the other player’s chosen stopping policy, each player selects a best response among her intra-personal equilibria. A resulting inter-personal equilibrium is then a Nash equilibrium between the two players, each of whom employs her best intra-personal equilibrium with respect to the other player’s stopping policy. Under appropriate conditions, we show that an inter-personal equilibrium exists, based on concrete iterative procedures along with Zorn’s lemma. To illustrate our theoretical results, we investigate a two-player real options valuation problem where two firms negotiate a deal of cooperation to initiate a project jointly. By deriving inter-personal equilibria explicitly, we find that coercive power in negotiation depends crucially on the impatience levels of the two firms.

     

企业利益相关者之间的合作博弈与均衡

企业不同的利益相关者之间存在合作博弈.企业利益相关者在反复的讨价还价博弈过程中逐步达到利益均衡,且博弈结果决定不同利益相关者对企业所有权的享有份额.本文在对利益相关者进行合理界定的基础上,运用合作博弈数学模型,求证利益相关者博弈的子博弈精炼纳什均衡解的唯一性.     

Risk trading,network topology and banking regulation

Abstract

In the context of understanding the nature of the risk transformation process of the financial system we propose an iterative risk-trading game between several agents who build their trading strategies based on a general utility setting. The game is studied numerically for different network topologies. Consequences of topology are shown for the wealth time-series of agents, for the safety and efficiency of various types of network. The proposed set-up allows an analysis of the effects of different approaches to banking regulation as currently suggested by the Basle Committee of Banking Supervision. We find a phase-transition-like phenomenon, where the Basle parameter plays the role of temperature and system safety serves as the order parameter. This result suggests the existence of an optimal regulation parameter. As a consequence, a tightening of the current regulatory framework does not necessarily lead to an improvement of the safety of the banking system. Moreover, we show that banking systems with local risk-sharing cooperations have higher global default rates than systems with low cyclicality.     

Liquidity protection versus moral hazard: the role of the IMF

A game between the IMF, a country and atomistic private investors is motivated by recent crises including that in Argentina. The one stage game has no Nash equilibrium in pure strategies. Considering an equilibrium in mixed strategies, conditions are derived on whether the IMF should exist. A “cooperative first best” may be supported in a repeated game by a “minimum punishment strategy” but breaks down as the probability of insolvency rises. Countries are likely to deviate in bad times placing the IMF in an “impossible position”. The international financial architecture (IFA) remains incomplete.     

我国税收征管方式的博弈分析

文章对我国基本的税收征管方式采用博弈论的方法进行分析。分别求出在这种征管方式下,任务博弈、礼品博弈、声誉博弈的均衡解。进一步求出征管博弈在任务博弈、礼品博弈、声誉博弈三个关联博弈约束条件下的子博弈精炼纳什均衡。指出这种征管方式存在的弊端,并依据分析所得结论提出改进这种征管方式的建议。