On risk averse competitive equilibrium

We discuss risked competitive partial equilibrium in a setting in which agents are endowed with coherent risk measures. In contrast to social planning models, we show by example that risked equilibria are not unique, even when agents’ objective functions are strictly concave. We also show that standard computational methods find only a subset of the equilibria, even with multiple starting points.     

Competitive equilibrium on risk exchanges: A constrained market approach

This paper concerns competitive equilibria on a market for risk exchanges (rex). Initially a short resume is offered of some fundamental results obtained in this field and essentially due to K. Borch. Much attention is devoted to the key question that equilibria could be seen as generated by a market working for contingent coverings (shortly an analytic approach) or by a simpler market for risks governed by a synthetic premium principle. The idea of rex markets constrained both on the quantity side as well as for the tarification system applied is then introduced as a useful tool to study e.g. markets where unconstrained equilibria turn out too complex. Finally an example of a non-traditional constrained market is briefly discussed.     

Mortality risk modeling: Applications to insurance securitization

This paper proposes a stochastic mortality model featuring both permanent longevity jump and temporary mortality jump processes. A trend reduction component describes unexpected mortality improvement over an extended period of time. The model also captures the uneven effect of mortality events on different ages and the correlations among them. The model will be useful in analyzing future mortality dependent cash flows of life insurance portfolios, annuity portfolios, and portfolios of mortality derivatives. We show how to apply the model to analyze and price a longevity security.     

Generalized gradients,bid–ask spreads,and market equilibrium

Abstract

This paper considers economies in which each agent valuates various goods by own generalized gradients. Taken together and appropriately scaled, the latter determine bid–ask spreads. When all such spreads are nil, market equilibrium prevails. Crucial for the arguments is a money commodity which denominates agents' rates of exchange or substitution. Equilibrium obtains when rates coincide across agents. The results may facilitate detailed modelling of market micro-structure, direct deals, and agent-based computations.     

On a market equilibrium theorem with an infinite number of commodities

A direct proof is given of the market equilibrium theorem of Gale, Nikaido and Debreu for an infinite-dimensional commodity space. The theorem is closely related to a recent result of Aliprantis and Brown, but allows for excess demand correspondences rather than excess demand functions.     

On simulation of optimal strategies and Nash equilibrium in the financial market context

Unlike physical time series, stock market prices may be affected by the predictions made by market participants with conflicting interests. This is the domain of game theory. Therefore, we propose a Stock Exchange Game Model (SEGM) to model this phenomenon. In SEGM, player strategies are to set their buying and selling levels for the next iteration via the autoregressive model AR(p) of order p selected by minimizing deviations from Nash Equilibrium (NE). NE represents the assumption of optimal behavior by market participants. The objective of SEGM is to simulate financial and other time series that are affected by predictions of the participants and to test the assumption of optimal player behavior, using a ‘virtual’ stock exchange. The simulation of SEGM suggests that NE is close to the Wiener model. This is a new explanation of the Random Walk (RW) model of the efficient market theory. To compare the simulation results with real data, the efficient market hypothesis was also tested, using financial time series of eight assets. The SEGM software is implemented in Java applets and can be run using a browser with Java support. The main web site is in .     

On Nash–Cournot oligopolistic market equilibrium models with concave cost functions

We consider Nash–Cournot oligopolistic market equilibrium models with concave cost functions. Concavity implies, in general, that a local equilibrium point is not necessarily a global one. We give conditions for existence of global equilibrium points. We then propose an algorithm for finding a global equilibrium point or for detecting that the problem is unsolvable. Numerical experiments on some randomly generated data show efficiency of the proposed algorithm.     

Electricity market equilibrium under information asymmetry

We study a competitive electricity market equilibrium with two trading stages, day-ahead and real-time. The welfare of each market agent is exposed to uncertainty (here from renewable energy production), while agent information on the probability distribution of this uncertainty is not identical at the day-ahead stage. We show a high sensitivity of the equilibrium solution to the level of information asymmetry and demonstrate economic, operational, and computational value for the system stemming from potential information sharing.     

On the additive completion of squares,II

Let B be a set of integers such that every n ≤ N can be written as n = b + λ² for some integer λ and b in B. Then, improving a result of the first author, we prove that |B| ≥ 1.245 √N.     

Analysis on the forward market equilibrium model

We establish the existence results for the Allaz-Vila [B. Allaz, J.-L. Vila, Cournot competition, forward markets and efficiency, J. Econ. Theory 59 (1993) 1-16] forward market equilibrium model when the M producers have different linear cost functions. We also consider an example with three asymmetric producers. The computational results supplement the conclusion in that the forward trading would increase market efficiency.     

Dynamic equilibrium formulation of the oligopolistic market problem

The aim of this paper is to generalize the oligopolistic market equilibrium problems when the data depend on time. We present results regarding the existence of solutions to such problems. Moreover, we show that continuity regularity results hold, and we use them in order to numerically solve the dynamic equilibrium problem.     

On an equilibrium problem with complementarity constraints formulation of pay-as-clear electricity market with demand elasticity

We consider a model of pay-as-clear electricity market based on a Equilibrium Problem with Complementarity Constraints approach where the producers are playing a noncooperative game parameterized by the decisions of regulator of the market (ISO). In the proposed approach the bids are assumed to be convex quadratic functions of the production quantity. The demand is endogenously determined. The ISO problem aims to maximize the total welfare of the market. The demand being elastic, this total welfare take into account at the same time the willingness to pay of the aggregated consumer, as well as the cost of transactions. The market clearing will determine the market price in a pay-as-clear way. An explicit formula for the optimal solution of the ISO problem is obtained and the optimal price is proved to be unique. We also state some conditions for the existence of equilibria for this electricity market with elastic demand. Some numerical experiments on a simplified market model are also provided.     

Insider trading equilibrium in a market with memory

We consider the Kyle-Back model for insider trading, with the difference that the classical Brownian motion noise of the noise traders is replaced by the noise of a fractional Brownian motion B ^H with Hurst parameter ${H>\frac{1}{2}}$ (when ${H=\frac{1}{2}, B^H}$ coincides with the classical Brownian motion). Heuristically, for ${H>\frac{1}{2}}$ this means that the noise traders has some ??memory??, in the sense that any increment from time t on has a positive correlation with its value at t. (In other words, the noise trading is a persistent stochastic process). It also means that the paths of the noise trading process are more egular than in the classical Brownian motion case. We obtain an equation for the optimal (relative) trading intensity for the insider in this setting, and we show that when ${H\rightarrow\frac{1}{2}}$ the solution converges to the solution in the classical case. Finally, we discuss how the size of the Hurst coefficient H influences the optimal performance and portfolio of the insider.     

一般均衡下基于产品市场和资本市场的单名CDS定价

次贷危机呼吁新的信用衍生品定价模型, 因此为存在产品市场和资本市场的经济结构建立一般均衡的单名CDS定价模型, 使用最优化求解一般均衡下的商品价格和CDS价格. 可以发现一般均衡的CDS定价具有资本市场和产品市场的因素, 这表示CDS的价格不再是由单纯的资本市场因素决定的, 而是由无风险利率、资本产出弹性、违约率、回收率同时决定的. 通过数量约束用模拟的方式研究多个均衡的动态变化, 发现违约风险的增加使得价格剧烈波动且市场交易萎缩. 在为以中国工商银行为参考资产的CDS定价过程中, 发现各种因素在不同的时期都可能成为定价的主要影响因素. 可以发现, 次贷危机的定价体系存在着信用调整问题和定价与实体经济脱节的问题. 可以认为, 一般均衡下基于产品市场和资本市场的单名CDS定价可以囊括多个市场的交叉影响, 为衍生品定价提供一个新的方向.     

A network formulation of market equilibrium problems and variational inequalities

This paper shows that market equilibrium problems of production may generally be modelled as equilibrium flow problems in networks and that their equilibrium conditions can be visualized as a variational inequality. This connection would allow us to transplant directly elements of the well-developed theory of equilibrium flow in networks to the theory of market equilibrium.