A chaotic gas-like model for trading markets

This paper considers the ideal gas-like model for trading markets, where each individual interacts with others trading in money-conservative collisions. Traditionally this model introduces different rules of random selection and exchange between pairs of agents, what leads to different money distributions in the community. Real economic transactions are complex but obviously non-random. Therefore, unlike the traditional model, this work introduces chaotic elements in the evolution of the economic system. As a result, it is found that the chaotic gas-like model can reproduce the referenced wealth distributions observed in real economies, i.e. the Gamma, Exponential and Pareto distributions.     

基于CCAPM框架的财富不平等与房价关系研究

运用含有房屋的CCAPM模型,在同时考虑房屋的消费属性与投资属性基础上分析了财富(或收入)分配对房价的影响;并通过数值模拟解释了我国房价高企的根源.结论表明,我国房价高企是财富分配不均所致,财富不均等程度加剧致使房屋从消费属性向投资属性转变进而推高了房价.文章也分析了财富分配对居民消费结构的影响,财富分配不均等程度加剧使得贫穷阶层的房屋消费比重下降而富裕阶层的投资性购房比重增加,进而拉高房价.文章最后指出,要调控我国当前房地产市场价格,必须从财富(或收入)分配入手,明晰产权.     

Convergence to an exponential wealth distribution in a random market model

We study the discrete-time model of López-Ruiz, López and Calbet, describing the evolution of a wealth distribution under random pairwise exchanges of wealth among agents. This requires the analysis of the behaviour of iterations of a non-linear operator defined on a space of probability distributions. We prove that, as conjectured by López-Ruiz, López and Calbet, starting from a general wealth distribution, the wealth distribution converges to the exponential equilibrium distribution. The proof employs a special metric defined on spaces of probability distributions through their Laplace transforms.     

A dynamic model of the distribution of wealth among households and nations

Stiglitz once showed that, in general, aggregate wealth is asymptotically uniformally distributed among individuals. However, in his formulation household saving is not the outcome of utility maximization over time. Constructing a simple dynamic general equilibrium model in which household saving is choice-theoretically determined, we show that given initial holdings of wealth there is a unique and stable steady state distribution of wealth and that the distribution of wealth becomes more even (resp. uneven) as time goes by if the total wealth is initially greater (resp. smaller) than its steady state level. We also study the response of the steady state equilibrium to the changes in initial distribution of wealth and the rate of time preference, and to several types of technological improvements.     

The distribution of wealth and the effect of extortion in structured populations

Despite that the heterogeneous distribution of wealth is widely observed in social, economical and biological system, few studies have been conducted to explore its influence on the evolutionary dynamics in populations. This paper discusses this problem by introducing a heterogeneous wealth allocation mechanism controlled by a tunable parameterα . Our study shows that there is a positive relationship between the level of cooperation and the extent of heterogeneity of wealth distribution. More importantly, we show that the catalytic effect of extortioners can be significantly strengthened if wealth is heterogeneously distributed among the whole population. Cooperators and extortioners can co-exist if the value of αis moderate. We explain this phenomenon by arguing that this heterogeneous allocation mechanism enables three types of strategists to form clusters around several rich cooperating neighbors initially. Clusters of defectors tend to be eliminated at early stages of evolution.     

Utility maximization, risk aversion, and stochastic dominance

Consider an investor trading dynamically to maximize expected utility from terminal wealth. Our aim is to study the dependence between her risk aversion and the distribution of the optimal terminal payoff. Economic intuition suggests that high risk aversion leads to a rather concentrated distribution, whereas lower risk aversion results in a higher average payoff at the expense of a more widespread distribution. Dybvig and Wang (J. Econ. Theory, 2011, to appear) find that this idea can indeed be turned into a rigorous mathematical statement in one-period models. More specifically, they show that lower risk aversion leads to a payoff which is larger in terms of second order stochastic dominance. In the present study, we extend their results to (weakly) complete continuous-time models. We also complement an ad-hoc counterexample of Dybvig and Wang, by showing that these results are “fragile”, in the sense that they fail in essentially any model, if the latter is perturbed on a set of arbitrarily small probability. On the other hand, we establish that they hold for power investors in models with (conditionally) independent increments.     

Calculating risk neutral probabilities and optimal portfolio policies in a dynamic investment model with downside risk control

This paper presents a method for solving multiperiod investment models with downside risk control characterized by the portfolio’s worst outcome. The stochastic programming problem is decomposed into two subproblems: a nonlinear optimization model identifying the optimal terminal wealth distribution and a stochastic linear programming model replicating the identified optimal portfolio wealth. The replicating portfolio coincides with the optimal solution to the investor’s problem if the market is frictionless. The multiperiod stochastic linear programming model tests for the absence of arbitrage opportunities and its dual feasible solutions generate all risk neutral probability measures. When there are constraints such as liquidity or position requirements, the method yields approximate portfolio policies by minimizing the initial cost of the replication portfolio. A numerical example illustrates the difference between the replicating result and the optimal unconstrained portfolio.     

Stochastic comparisons of distorted variability measures

In this paper, we consider the dispersive order and the excess wealth order to compare the variability of distorted distributions. We know from Sordo (2009a) that the excess wealth order can be characterized in terms of a class of variability measures associated to the tail conditional distribution which includes, as a particular measure, the tail variance. Given that the tail conditional distribution is a particular distorted distribution, a natural question is whether this result can be extended to include other classes of variability measures associated to general distorted distributions. As we show in this paper, the answer is yes, by focusing on distorted distributions associated to concave distortion functions. For distorted distributions associated to more general distortions, the characterizations are stated in terms of the stronger dispersive order.     

Adaptive control of three continuous-time portfolio and consumption models

An economic application of adaptive control is presented using three continuous time portfolio and consumption models that are natural generalizations of a model of Merton. In these models of the wealth of an individual investor, it is assumed that the various parameters are deterministic functions of time or stochastic processes. An adaptive control problem arises for each of these models when it is assumed that the average return rate of the risky asset, which is either a deterministic function or a stochastic process, is not observed. For these models, a recursive family of estimators of the average return rate of the risky asset is given based on the observations of the wealth. These estimates are used in the control of the wealth equation.This research was partially supported by NSF Grant No. ECS-84-03286-A01 and by University of Kansas General Research Allocation No. 3806-XO-0038.     

Less is more: Increasing retirement gains by using an upside terminal wealth constraint

We solve a portfolio selection problem of an investor with a deterministic savings plan who aims to have a target wealth value at retirement. The investor is an expected power utility-maximizer. The target wealth value is the maximum wealth that the investor can have at retirement.By constraining the investor to have no more than the target wealth at retirement, we find that the lower quantiles of the terminal wealth distribution increase, so the risk of poor financial outcomes is reduced. The drawback of the optimal strategy is that the possibility of gains above the target wealth is eliminated.     

Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint

The complexity of financial markets leads to different types of indeterminate asset returns. For example, asset returns are considered as random variables, when the available data is enough. When the available data is too small or even no available data to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degrees of asset returns. Then, asset returns can be described as uncertain variables. In this paper, we discuss a multi-period portfolio selection problem under uncertain environment, which maximizes the final wealth and minimizes the risk of investment. Unlike the common method to describe the multi-period portfolio selection problem as a bi-objective optimization model, we formulate this uncertain multi-period portfolio selection problem by a new method in three steps with two single objective optimization models. And, we consider the influence of transaction cost and bankruptcy of investor. Then, the proposed uncertain optimization models are transformed into the corresponding crisp optimization models and we use the genetic algorithm combined with penalty function method to solve them. Finally, a numerical example is given to show the effectiveness and practicability of proposed models and method.     

The ease of generating chaotic behavior in economics

Supported by the wealth of models demonstrating chaotic behavior in economics, it becomes appropriate to examine whether this phenomenon is restricted to concocted models or is central to economics. After showing why this behavior is prevalent, aspects of economics causing this behavior are identified. Surprisingly, the basic source of problems from choice theory also generate some of the random motion of economics.     

Habit formation and resource dependence in dynastic economies

This paper studies the consequences of habit formation in dynastic economies that exploit exhaustible resources. If the strength of habits is below a critical level, positive bequests generate Ramsey-Stiglitz equilibria: the altruism factor determines long-run growth and habits increase output levels by increasing capital accumulation and smoothing resource extraction during the transition. If the strength of habits is above the threshold, zero bequests induce Diamond-Mourmouras equilibria: the transitional effects become permanent and habits increase long-run growth. Results differ from those of capital-labor models because resource dependence implies that long-run growth is determined by the intergenerational distribution of wealth.     

Some applications of L2-hedging with a non-negative wealth process

We consider the problem of L ²-hedging of contingent claims in diffusion type models for securities markets. In contrast to a recent paper of Schweizer (1994) we insist on a non-negative wealth process corresponding to the optimal hedge portfolio. For this reason the usual projection methods cannot be applied. We give some applications of L ²-hedging in this setting including hedging under constraints, a problem of approximating the wealth process of a richer investor and a mean-variance version of it.     

NA样本下Pareto分布参数的经验Bayes估计

讨论了Pareto分布在平方损失下参数的Bayes估计,采用同分布负相协样本的核估计方法讨论了参数的经验Bayes(EB)估计问题,并计算了给定条件下参数的经验Bayes估计的收敛速度。最后,对我国高收入阶层的财富分布情况进行了实证分析,实证分析表明我国高收入阶层的财富分布是可以用Pareto分布来描述的。     

Modeling attitudes towards uncertainty and risk through the use of choquet integral

The aim of this paper is to present in a unified framework a survey of some results related to Choquet Expected Utility (CEU) models, a promising class of models introduced separately by Quiggin [35], Yaari [48] and Schmeidler [40, 41] which allow to separate attitudes towards uncertainty (or risk) from attitudes towards wealth, while respecting the first order stochastic dominance axiom.     

On expected utility for financial insurance portfolios with stochastic dependencies

The effect of background risks as human capital, market risks and catastrophic events has been considered in the literature in different contexts. In this note, we consider financial insurance portfolios with insurable risks and one background risk (uninsurable financial asset), such that the random losses and the background risk depend on environmental parameters. We study how dependencies between the risks influence the expected utility of the portfolio’s wealth distribution under risk aversion, when the environmental parameters are random. Stochastic bounds for the expected wealth are given from modeling the dependence between the parameters by different notions. Similar results are given for multivariate portfolios with n groups and multivariate risk aversion, besides an expected utility comparison result for the minimum and the total portfolio’s wealth.     

Asymptotics of homogeneous oscillations in a compressible viscous fluid

The large amplitude high frequency oscillations of the flow of a compressible viscous fluid have been shown to obey to an integro-differential system. We consider here the case of homogeneous oscillations, with both gas-like pressure law and a van der Waals one. We show that the solution admits a limit as the time increases. This limit is constant in the former case, but may take up to three distinct values in the latter.     

激励机制和VaR约束下的DC养老金计划的最优投资

研究了DC养老金经理在单一管理费以及混合收费(同时收取管理费与绩效费)这两种不同的薪酬机制和损失厌恶下的最优投资组合问题。利用凹化方法得到了存在终端财富约束下的最优财富过程和最优投资策略的解析表达式。数值结果表明损失厌恶,VaR约束和薪酬机制会极大地影响最优终端财富的分布。特别地,在决策参照点较高时,损失厌恶会导致混合薪酬机制下最优终端财富的尾部风险较低。     

Mean-risk portfolio management with bankruptcy prohibition

In accordance with Solvency II, the commonly tightened government regulation on insurance cooperations, they have been obligated to take conservative investment strategies such as those ruling out the possibility of bankruptcy. With this in mind, in this article, we aim to continue our work (Wong et al., 2017a,b) . First, we study the solvability of mean-risk portfolio optimization problem with bankruptcy prohibition, in the complete market in which the investor aims to maximize the expected payoff and to minimize the deviation risk simultaneously, which is of great use in the insurance paradigm. Secondly, we also provide the original weak convergence result of the optimal terminal wealth of a sequence of approximate markets to that of the limiting market through their corresponding pricing kernels. As a result, we establish an effective numerical algorithm calibrating the optimal terminal wealth under Black–Scholes models by that of binomial tree models. The results of our numerical simulations indicate that the downside risk of the optimal payoff can be effectively reduced by imposing the bankruptcy prohibition.