Closed-loop Nash competition for liquidity

We study a multiplayer stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. In this context, we prove that a closed-loop Nash equilibrium exists if the price impact parameter is small enough. Compared to the corresponding open-loop Nash equilibrium, both the agents' optimal trading rates and their performance move towards the central-planner solution, in that excessive trading due to lack of coordination is reduced. However, the size of this effect is modest for plausible parameter values.     

Global monetary policy under a dollar standard

This paper derives an optimal monetary policy in a world with a dollar standard, defined as an environment in which all traded goods prices are set in US dollars, so that exchange rate pass-through into the US price level is zero. We show that the US is essentially indifferent to exchange rate volatility, while the rest of the world places a high weight on exchange rate volatility. In a Nash equilibrium of the monetary policy game, US preferences dominate; the equilibrium is identical to one where the US alone chooses world monetary policy. Despite this, we find surprisingly that the US loses from the dollar's role as an international currency, since the absence of exchange rate pass-through leads to inefficient expenditure allocations within the US. Finally, we derive the conditions for a dollar standard to exist.     

A STATE‐CONSTRAINED DIFFERENTIAL GAME ARISING IN OPTIMAL PORTFOLIO LIQUIDATION

We consider n risk‐averse agents who compete for liquidity in an Almgren–Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear quadratic differential game with state constraints. The state constraints enter the problem as terminal boundary conditions for finite and infinite time horizons. We prove existence and uniqueness of Nash equilibria and give closed‐form solutions in some special cases. We also analyze qualitative properties of the equilibrium strategies and provide corresponding financial interpretations.     

A Sealed-Bid Two-Attribute Yardstick Auction Without Prior Scoring

We analyze a two-attribute single item procurement auction that uses yardstick competition to settle prices. The auction simplifies the procurement process by reducing the principal’s articulation of preferences to simply choosing the most preferred offer as if it was a market with posted prices. This is done simply by replacing the submitted sealed bids by yardstick bids, computed by a linear weighting of the other participants’ bids. We show that there is only one type of Nash equilibria where some agents may win the auction by submitting a zero price-bid. Using a simulation study we demonstrate that following this type of equilibrium behavior often leads to winner’s curse. The simulations show that in auctions with more than 12 participants the chance of facing winner’s curse is around 95 %. Truthful reporting, on the other hand, does not constitute a Nash equilibrium but it is ex post individually rational. Using a simulation study we demonstrate that truthful bidding may indeed represent some kind of focal point.     

IDENTIFYING THE LINDAHL EQUILIBRIUM WITHOUT TRANSFERS AS A SOCIAL OPTIMUM

The Lindahl equilibrium is an important solution concept in economies with externalities or public goods. In this paper, a ‘Negishi‐type’ theorem that connects the Lindahl equilibrium without transfers with the social optimum solution is proposed and proved. The theorem states that the solution of a social planner's problem with the social welfare weights proportional to the inverse of the private shadow prices of externalities in an auxiliary Nash equilibrium is the Lindahl equilibrium without transfers. To verify the theorem constructively, an algorithm for finding the Lindahl equilibrium is developed. Its efficacy is demonstrated through a numerical example.     

A NONZERO‐SUM GAME APPROACH TO CONVERTIBLE BONDS: TAX BENEFIT,BANKRUPTCY COST,AND EARLY/LATE CALLS

Convertible bonds are hybrid securities that embody the characteristics of both straight bonds and equities. The conflicts of interest between bondholders and shareholders affect the security prices significantly. In this paper, we investigate how to use a nonzero‐sum game framework to model the interaction between bondholders and shareholders and to evaluate the bond accordingly. Mathematically, this problem can be reduced to a system of variational inequalities and we explicitly derive the Nash equilibrium to the game. Our model shows that credit risk and tax benefit have considerable impacts on the optimal strategies of both parties. The shareholder may issue a call when the debt is in‐the‐money or out‐of‐the‐money. This is consistent with the empirical findings of “late and early calls.” In addition, the optimal call policy under our model offers an explanation for certain stylized patterns related to the returns of company assets and stocks on call.     

自利行为下我国遭遇反倾销诉讼原因的博弈分析

自上世纪90年代以来我国一直是美欧等西方发达国家反倾销的重点国家,这引起了我国学者对于倾销与反倾销的广泛研究。本文从自利行为角度对国企出口遭遇反倾销进行探讨。通过模型建构,得出结论:由于信息的不完全性,这使得进口方更容易错误地认为出口方有倾销行为。     

THE STOCHASTIC VOLATILITY MODEL OF BARNDORFF‐NIELSEN AND SHEPHARD IN COMMODITY MARKETS

We consider the non‐Gaussian stochastic volatility model of Barndorff‐Nielsen and Shephard for the exponential mean‐reversion model of Schwartz proposed for commodity spot prices. We analyze the properties of the stochastic dynamics, and show in particular that the log‐spot prices possess a stationary distribution defined as a normal variance‐mixture model. Furthermore, the stochastic volatility model allows for explicit forward prices, which may produce a hump structure inherited from the mean‐reversion of the stochastic volatility. Although the spot price dynamics has continuous paths, the forward prices will have a jump dynamics, where jumps occur according to changes in the volatility process. We compare with the popular Heston stochastic volatility dynamics, and show that the Barndorff‐Nielsen and Shephard model provides a more flexible framework in describing commodity spot prices. An empirical example on UK spot data is included.     

OPTIMAL DYNAMIC PROFIT TAXATION: THE DERIVATION OF FEEDBACK STACKELBERG EQUILIBRIA

In this paper we develop a framework for determining optimal profit taxation for a welfare maximising government. We show that there is a dynamic trade off between public consumption now and in the future. Two possible solutions are derived. The first solution, which is the formal outcome of an open-loop Stackelberg equilibrium of a game between government and firms, is time-inconsistent. The second solution, which corresponds to a feedback Stackelberg equilibrium, is time-consistent, but yields a lower value of steady-state utility. The outcome of the feedback Stackelberg equilibrium depends on the number of firms in this economy. If the number of firms is large, this equilibrium coincides with the open-loop Nash equilibrium. Furthermore, we show the dynamic paths if the economy goes from its feedback to its open-loop steady-state.     

An explicitly solvable multi‐scale stochastic volatility model: Option pricing and calibration problems

We introduce an explicitly solvable multiscale stochastic volatility model that generalizes the Heston model. The model describes the dynamics of an asset price and of its two stochastic variances using a system of three Ito stochastic differential equations. The two stochastic variances vary on two distinct time scales and can be regarded as auxiliary variables introduced to model the dynamics of the asset price. Under some assumptions, the transition probability density function of the stochastic process solution of the model is represented as a one‐dimensional integral of an explicitly known integrand. In this sense the model is explicitly solvable. We consider the risk‐neutral measure associated with the proposed multiscale stochastic volatility model and derive formulae to price European vanilla options (call and put) in the multiscale stochastic volatility model considered. We use the thus‐obtained option price formulae to study the calibration problem, that is to study the values of the model parameters, the correlation coefficients of the Wiener processes defining the model, and the initial stochastic variances implied by the “observed” option prices using both synthetic and real data. In the analysis of real data, we use the S&P 500 index and to the prices of the corresponding options in the year 2005. The web site http://www.econ.univpm.it/recchioni/finance/w7 contains some auxiliary material including some animations that helps the understanding of this article. A more general reference to the work of the authors and their coauthors in mathematical finance is the web site http://www.econ.univpm.it/recchioni/finance . © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:862–893, 2009     

MEAN–VARIANCE PORTFOLIO OPTIMIZATION WITH STATE‐DEPENDENT RISK AVERSION

The objective of this paper is to study the mean–variance portfolio optimization in continuous time. Since this problem is time inconsistent we attack it by placing the problem within a game theoretic framework and look for subgame perfect Nash equilibrium strategies. This particular problem has already been studied in Basak and Chabakauri where the authors assumed a constant risk aversion parameter. This assumption leads to an equilibrium control where the dollar amount invested in the risky asset is independent of current wealth, and we argue that this result is unrealistic from an economic point of view. In order to have a more realistic model we instead study the case when the risk aversion depends dynamically on current wealth. This is a substantially more complicated problem than the one with constant risk aversion but, using the general theory of time‐inconsistent control developed in Björk and Murgoci, we provide a fairly detailed analysis on the general case. In particular, when the risk aversion is inversely proportional to wealth, we provide an analytical solution where the equilibrium dollar amount invested in the risky asset is proportional to current wealth. The equilibrium for this model thus appears more reasonable than the one for the model with constant risk aversion.     

On utility maximization under model uncertainty in discrete‐time markets

We study the problem of maximizing terminal utility for an agent facing model uncertainty, in a frictionless discrete‐time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the utility function, defined either on the positive real line or on the whole real line, is bounded from above. We further find that the boundedness assumption can be dropped, provided that we impose suitable integrability conditions, related to some strengthened form of no‐arbitrage. These results are obtained in an alternative framework for model uncertainty, where all possible dynamics of the stock prices are represented by a collection of stochastic processes on the same filtered probability space, rather than by a family of probability measures.     

Strategic Interactions in a Growth Model with Infrastructure Capital

A dynamic game growth model with infrastructure capital is analyzed and it is shown that the pattern of growth can be either endogenous or exogenous depending on agents’ commitment behavior. If the agents commit their future actions, there is a unique Nash equilibrium with endogenous growth. However, if they cannot commit their future actions and they condition their actions on the state variable at each time, then for any level of infrastructure capital there exist infinitely many equilibria: some of them exhibit endogenous growth and others show no growth in the long run (or even in the short run).     

Why is the Doha Development Agenda Failing? And What Can Be Done? A Computable General Equilibrium–Game Theoretical Approach

We use a world computable general equilibrium model to simulate 143 potential trade reforms and seek solutions to the issues hampering progress in the Doha Development Agenda (DDA). Inside the domain defined by all these possible outcomes, we apply the axiomatic theory of bargaining and select the Nash solution of cooperative games. The solutions vary according to the objective functions adopted by the trade negotiators. When real income is the objective and services are excluded, or when optimising terms of trade is the objective, the Nash solution is the status quo. Trade liberalisation is feasible only when the negotiators focus on national exports or gross domestic product (GDP). Our assessment of some possible solutions reveals that excluding members having a GDP below a certain threshold improves the bargaining process, regardless of the governments’ objective. Formation of coalition, such as the G20, constitutes an option for its members to block outcomes imposed by rich members. We also find that side payments may be a solution, but represent a very high share of the global income gain.     

Risk Minimization with Incomplete Information in a Model for High‐Frequency Data

We study risk‐minimizing hedging‐strategies for derivatives in a model where the asset price follows a marked point process with stochastic jump‐intensity, which depends on some unobservable state‐variable process. This model reflects stylized facts that are typical for high frequency data. We assume that agents in our model are restricted to observing past asset prices. This poses some problems for the computation of risk‐minimizing hedging strategies as the current value of the state variable is unobservable for our agents. We overcome this difficulty by a two‐step procedure, which is based on a projection result of Schweizer and show that in our context the computation of risk‐minimizing strategies leads to a filtering problem that has received some attention in the nonlinear filtering literature.     

ARROW–DEBREU EQUILIBRIA FOR RANK‐DEPENDENT UTILITIES

We provide conditions on a one‐period‐two‐date pure exchange economy with rank‐dependent utility agents under which Arrow–Debreu equilibria exist. When such an equilibrium exists, we show that the state‐price density is a weighted marginal rate of intertemporal substitution of a representative agent, where the weight depends on the differential of the probability weighting function. Based on the result, we find that asset prices depend upon agents' subjective beliefs regarding overall consumption growth, and we offer a direction for possible resolution of the equity premium puzzle.     

Randomized Stopping Times and American Option Pricing with Transaction Costs

In a general discrete-time market model with proportional transaction costs, we derive new expectation representations of the range of arbitrage-free prices of an arbitrary American option. The upper bound of this range is called the upper hedging price, and is the smallest initial wealth needed to construct a self-financing portfolio whose value dominates the option payoff at all times. A surprising feature of our upper hedging price representation is that it requires the use of randomized stopping times (Baxter and Chacon 1977), just as ordinary stopping times are needed in the absence of transaction costs. We also represent the upper hedging price as the optimum value of a variety of optimization problems. Additionally, we show a two-player game where at Nash equilibrium the value to both players is the upper hedging price, and one of the players must in general choose a mixture of stopping times. We derive similar representations for the lower hedging price as well. Our results make use of strong duality in linear programming.     

Lévy betas: Static hedging with index futures

This study considers calibration to forward‐looking betas by extracting information on equity and index options from prices using Lévy models. The resulting calibrated betas are called Lévy betas. The objective of the proposed approach is to capture market expectations for future betas through option prices, as betas estimated from historical data may fail to reflect structural change in the market. By assuming a continuous‐time capital asset pricing model (CAPM) with Lévy processes, we derive an analytical solution to index and stock options, thus permitting the betas to be implied from observed option prices. One application of Lévy betas is to construct a static hedging strategy using index futures. Employing Hong Kong equity and index option data from September 16, 2008 to October 15, 2009, we show empirically that the Lévy betas during the sub‐prime mortgage crisis period were much more volatile than those during the recovery period. We also find evidence to suggest that the Lévy betas improve static hedging performance relative to historical betas and the forward‐looking betas implied by a stochastic volatility model.     

基于最大边缘分配算法的雷达博弈波形设计

实战背景下雷达目标先验信息有较大的不确定性,基于先验信息设计的波形不能满足参数估计的需要。为解决该问题,提出了一种博弈条件下的雷达波形设计方法。考虑到雷达与干扰机在电子对抗中的非同时性,采用Stackelberg博弈框架进行建模。该方法以优化雷达能量谱分布为策略,采用最大互信息准则建立效用函数。博弈过程中,雷达与干扰机各自根据对手策略优化发射波形,经过多次迭代,双方达到纳什均衡。仿真实验对比了均衡策略与maxmin策略与随机策略,证实了所提算法的有效性。