Complex dynamics in equilibrium asset pricing models with boundedly rational,heterogeneous agents

We study a simple model based upon the Lucas framework where heterogeneous agents behave rationally in a fully intertemporal setting but do not know other investors' personal preferences, wealth or investment portfolios. As a consequence, agents initially do not know the equilibrium asset pricing function and must make guesses, which they update via adaptive learning with constant gain. We demonstrate that even in this simple environment the economy can, depending on parameters, exhibit either stable convergence to equilibrium, or chaotic dynamical behavior of asset prices and trading volume without converging to the rational expectations equilibrium of the Lucas model. This contradicts the assertion that the Lucas model is stable in the face of modest deviations from the strong assumptions required to compute the equilibrium. © 2013 Wiley Periodicals, Inc. Complexity 19: 38–55, 2014     

Portfolio Selection Problem with Minimax Type Risk Function

The investor's preference in risk estimation of portfolio selection problems is important as it influences investment strategies. In this paper a minimax risk criterion is considered. Specifically, the investor aims to restrict the standard deviation for each of the available stocks. The corresponding portfolio optimization problem is formulated as a linear program. Hence it can be implemented easily. A capital asset pricing model between the market portfolio and each individual return for this model is established using nonsmooth optimization methods. Some numerical examples are given to illustrate our approach for the risk estimation.     

基于粗集理论的组合预测法在无形资产评估中的应用

针对如何评估企业无形资产的问题,运用基于粗集理论的组合预测方法,建立了企业无形资产评估的数量模型。该模型的特点是将组合预测方法中权系数的确定问题转化为粗集理论中的属性重要性评价问题,这样就在很大程度上克服了传统组合预测方法中权系数确定主观性太大的缺陷,而使得权系数的确定更具客观性。最后,结合实例阐述了基于粗集理论的组合预测方法在企业无形资产评估中的应用,进一步说明了该方法的可行性和有效性。     

Capital Asset Pricing Model (CAPM) with drawdown measure

The notion of drawdown is central to active portfolio management. Conditional Drawdown-at-Risk (CDaR) is defined as the average of a specified percentage of the largest drawdowns over an investment horizon and includes maximum and average drawdowns as particular cases. The necessary optimality conditions for a portfolio optimization problem with CDaR yield the capital asset pricing model (CAPM) stated in both single and multiple sample-path settings. The drawdown beta in the CAPM has a simple interpretation and is evaluated for hedge fund indices from the HFRX database in the single sample-path setting. Drawdown alpha is introduced similarly to the alpha in the classical CAPM and is evaluated for the same hedge fund indices. Both drawdown beta and drawdown alpha are used to prioritize hedge fund strategies and to identify instruments for hedging against market drawdowns.     

Black-Litterman投资组合模型的进一步推导分析

在理论上通过推导首次得出了Black-Litterman模型(B-L模型)最优权重与信心水平的公式.在各资产收益不相关及单一绝对观点的假设下,得出各资产的B-L模型最优权重与信心水平的简化表达式.借助于此,还对信心水平与最优权重公式的进一步理论分析,并以光大证券的"乌龙指"做实证,详细分析投资者在没有市场观点、拥有内幕信息、以及信心水平在某范围变化时,其所持各投资品权重的特点.     

动态资产份额定价理论模型

运用倒向随机微分方程数学方法 ,建立了动态资产份额定价理论模型 .这一模型是资产份额定价法的改进 .求解模型得到动态资产份额定价理论公式 ,并得出结论 :资产份额定价公式完全可以作为特例 ,以离散时间意义和在不考虑动态投资的情况下 ,由动态资产份额定价理论公式得到 .     

金融资产收益分布的混合高斯分析

本文研究了金融资产收益的混合高斯分布模型 ,给出了混合高斯分布的 Kolmogorov-Smirnov检验的方法 ,分析了金融资产收益的非高斯性及市场价格运动的有效性 .此外 ,用成分数目 K*、拟合误差 DK*n和主成分系数 p*k 描述金融资产收益的性质 ,对外汇银行同业拆借市场和中国股票市场实证分析     

Optimal assets allocation and benefit outgo policies of DC pension plan with compulsory conversion claims

In this paper, we study optimal asset allocation and benefit outgo policies of DC (defined contribution) pension plan. We extend He and Liang model (2013a,b) to describe dynamics of individual fund scale during distribution period. The fund scale is affected by investment return, benefit outgo and mortality credit. The management of the pension plan controls the asset allocation and benefit outgo policies to achieve the objective of pension members. The goal of the management is to minimize accumulated deviations between the actual benefit outgo and a pre-set target during the whole distribution period. The performance function (criterion) is the weighted average of the square and linear deviations to express more penalty on negative deviation than positive deviation. Using HJB (Hamilton–Jacobi–Bellman) equations and variational inequality methods, the closed-forms of the optimal policies are derived. The counterintuitive effect of the optimal proportion allocated in the risky asset with respect to the fund scale is also derived, and the optimal benefit outgo has the form of the spread method. Moreover, we use Monte Carlo Methods (MCM) to analyze economic behaviors of the optimal asset allocation and benefit outgo policies.     

Asset pricing for an affine jump‐diffusion model using an FD method of lines on nonuniform meshes

We present a novel numerical scheme for the valuation of options under a well‐known jump‐diffusion model. European option pricing for such a case satisfies a 1 + 2 partial integro‐differential equation (PIDE) including a double integral term, which is nonlocal. The proposed approach relies on nonuniform meshes with a focus on the discontinuous and degenerate areas of the model and applying quadratically convergent finite difference (FD) discretizations via the method of lines (MOL). A condition for observing the time stability of the fully discretized problem is given. Also, we report results of numerical experiments.     

关于无风险资产不存在时资产组合选择的研究

以往关于资产组合选择的研究大多假设市场上存在无风险资产,但无风险资产实际上是不存在的.当不存在无风险资产时,假设投资者的效用定义在消费上,消费一直是投资者财富的一个固定比例,投资者的最优资产组合由两部分组成:短视的资产组合和对冲组合.假设只有股票和债券两种风险资产,当股票和债券的风险具有负的相关性时,投资者现在会消费更多,同时也会在股票上投资更多;两者正相关时,投资者无法降低风险,会减持股票并降低当前消费;两者不相关时,投资者持有的股票权重和存在无风险资产时一样.最后,还推导出了多种资产情况下最优消费和资产组合的解析表达式.