具有一般效用函数与允许卖空的资本市场中均衡价格向量的存在性与唯一性

对有有限多个其效用函数为一般凹函数的投资者参与的资本市场，在假设风险资产收益的联合分布为椭圆分布之下，通过考虑期望效用最大化问题，我们导出了使市场出清的均衡价格向量存在唯一的条件及其计算公式，并简要讨论了所给条件的经济意义，所得结果推广了有关资产市场均衡分析的某些结果。     

基于矩分析的资产组合选择

在风险资产收益分布为非正态的情景下,通过矩分析,研究其收益的高阶矩对资产组合选择的影响.首先,假设风险资产收益存在有限阶矩,泰勒展开边际财富期望效用,获得静态资产组合选择的近似解;其次,假设收益过程的跳跃产生收益分布的非正态性,运用随机控制方法获得动态资产组合选择的近似解析解,从高阶矩角度解释其特征。分析表明,超出峰度的存在导致减少风险资产投资,正(负)的偏度导致增加(减少)风险资产投资,该影响性随着它们及风险规避系数的增大而增强;可预测性导致资产组合存在正或负的对冲需求,取决于相关系数的符号和风险规避系数;跳跃性总体上减少风险资产投资;可预测性和跳跃性对动态资产组合选择的影响具有内在关联性。     

极大极小投资组合选择模型和均衡价格系统

讨论了市场上不存在无风险资产条件下投资组合选择的极大极小模型,推导出市场上不存在无风险资产时极大极小模型的最优投资策略和有效前沿,得到了资本市场均衡时存在唯一的非负均衡价格系统的充分必要条件和各资产均衡价格的解析表达式.     

违约市场中的n个保险公司的最优投资和再保险问题（英文）

本文研究了n个保险公司之间的非零和随机微分投资再保险博弈问题.每个保险公司可以购买比例再保险,并将财富投资于一个由无风险资产,可违约债券和n个风险资产组成的金融市场.特别地,风险资产的价格过程服从CEV模型,可违约债券可在违约时收回一定比例的价值.每个保险公司的目标是相对于竞争对手,最大化终端财富的期望指数效用.利用随机最优控制理论,我们分别推导了均衡策略和均衡值函数的显式表达式.数值例子分析了模型参数对均衡策略的影响.此外,我们还分析了保险公司数量对均衡投资策略的影响.我们发现,随着保险公司数量的增加,每个保险公司将在风险资产和可违约债券上投入更多的资金.     

Heston随机波动率模型下带负债的投资组合博弈

本文研究了Heston随机波动模型下两个投资人之间的随机微分投资组合博弈问题。假设金融市场上存在价格过程服从常微分方程的无风险资产和价格过程服从Heston随机波动率模型的风险资产。该博弈问题被构造成两个效用最大化问题,每个投资者的目标是最大化终止时刻个人财富与竞争对手财富差的效用。首先,我们应用动态规划原理,得出了相应值函数所满足的HJB方程。然后,得到了在幂期望效用框架下非零和博弈的均衡投资策略和值函数的显式表达。最后,借助数值模拟,分析了模型中的参数对均衡投资策略和值函数的影响,从而为资产负债管理提供一定的理论指导。     

具有单向转载的Newsboy型产品订货决策的博弈模型

研究了允许单向横向转载的Newsboy型产品的订货决策问题。以两个Newsboy型零售商为研究对象,在允许单向横向转载存在的前提下,构建了以二者期望利润最大化为目标的非合作博弈模型,讨论了模型存在纳什均衡解的条件并证明了解的存在性与唯一性,给出了均衡解的解析表达形式,进一步分析了转载价格对均衡的影响。最后的算例分析则从期望利润、均衡订货和转载价格三个方面验证了横向转载策略的优势。研究表明:(1)与传统报童模型相比,横向转载策略提高了零售商的期望利润;(2)转载价格显著影响横向转载策略下零售商的订货决策。     

选择资产组合的EP-MV模型及最优解的解析表示

本文提出了存在无风险资产贷出或借入时的有效投资组合模型(EP-MV模型)，研究了不允许卖空(投资比例非负)约束条件下，EP-MV优化模型的算法，给出了有效投资组合投资比例的解析表示．在资产收益由多因素模型产生的基础上，得到了资产与有效投资组合的期望收益及风险的估计，便于实际应用．     

逆向选择与伯川德竞争下两期保险完全分离均衡

多期保险作为单期保险自选机制的一种补充,是一种重要的动态风险分类方法,有利于控制逆向选择风险.在伯川德竞争假设下,研究两期保险完全分离均衡存在的充要条件.首先,建立了两期保险问题的动态博弈模型,然后,通过分析投保人的激励相容约束与个人合理性约束推导出完全分离均衡存在的充要条件,并在直观标准下对均衡结果进行精炼,论证结果表明,这一最优均衡使得信号传递成本达到最小.     

常数相对风险厌恶多单位拍卖的比较静态与定价结构

考虑竞价者具有常数相对风险厌恶时的多单位拍卖问题,讨论均衡出价与风险偏好以及价值分布之间的关系.在竞价者具有相同的风险偏好的对称拍卖情形,利用风险中性等价导出了比较静态的充要条件,这一充要条件综合了风险偏好和价值分布的变化.在竞价者具有不同的风险偏好的非对称拍卖中,导出了均衡出价关于风险偏好的线性定价结构,依据这一结构,对任意给定出价,竞价者要求的剩余是其风险厌恶参数的线性函数,并且可以分解为竞争性剩余和风险厌恶剩余.     

客户终生价值的蒙特卡罗分析

客户终生价值分析是客户关系管理研究的重要课题．但现有的研究只限于于期望值分析，而忽略了客户价值的风险。本文使用贝叶斯方法及蒙特卡罗方法分析客户终生价值及客户资产，可以得到个体客户终生价值和客户资产的后验分布样本。分析的结果揭示了具有相近期望价值的客户，其风险可能存在较大差异，为客户选择决策提供了依据。     

t-分布与不同风险度量下有效投资组合及其边缘的相互关系研究

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivari-ate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

跳扩散环境下考虑红利支付的动态资产配置问题研究

研究资产价格带跳环境下红利支付对投资者资产配置的影响,投资者将其财富在风险资产和无风险资产中进行分配,在终端财富预期效用最大化标准下,利用动态规划原理建立的HJB方程推导最优配置策略,并得到最优动态资产配置策略的近似解.最后通过数值模拟,分析了跳和红利支付对投资者最优配置策略的影响.结果表明在跳发生的情况下,不管跳的大小和方向如何,投资者都会减少其在风险资产中的配置头寸,同时带有红利支付的资产比不带红利支付的资产对投资者更具吸引力.     

Asset allocation with distorted beliefs and transaction costs

In this paper we study the problem of the optimal portfolio selection with transaction costs for a decision-maker who is faced with Knightian uncertainty. The decision-maker’s portfolio consists of one risky and one risk-free asset, and we assume that the transaction costs are proportional to the traded volume of the risky asset. The attitude to uncertainty is modeled by the Choquet expected utility. We derive optimal strategies and bounds of the no-transaction region for both optimistic and pessimistic decision-makers. The no-transaction region of a pessimistic investor is narrower and its bounds lie closer to the origin than that of an optimistic trader. Moreover, under the Choquet expected utility the structure of the no-transaction region is not necessarily a closed interval as it is under the standard expected utility model.     

The impact of fat tailed returns on asset allocation

This paper analyzes the asset allocation problem of an investor who can invest in equity and cash when there is time variation in expected returns on the equity. The solution methodology is multistage stochastic asset allocation problem with decision rules. The uncertainty is modeled using economic scenarios with Gaussian and stable Paretian non-Gaussian innovations. The optimal allocations under these alternative hypothesis are compared. Our computational results suggest that asset allocation may be up to 20% different depending on the utility function and the risk aversion level of the investor. Certainty equivalent return can be increased up to .13% and utility can be improved up to .72% by switching to the stable Paretian model.     

Taylor series approximations to expected utility and optimal portfolio choice

This paper revisits the subject of Taylor series approximations to expected utility and investigates the applicability of the technique to optimal portfolio choice problems. We first provide conditions under which the approximate expected utility of a given portfolio converges to its exact counterpart. We then extend the analysis to the optimal portfolio choice setting and provide conditions on the distribution of asset returns under which the solution to the approximate portfolio choice problem converges to its exact counterpart. Finally, we show that, when asset returns are skewed, one can improve the precision and efficiency of the Taylor expansion by applying a simple nonlinear transformation to asset returns designed to symmetrize the transformed return distribution and shrink its support.     

CEV模型下时滞最优投资与再保险问题

在常方差弹性（constant elasticity of variance,CEV）模型下考虑了时滞最优投资与比例再保险问题.假设保险公司通过购买比例再保险对保险索赔风险进行管理,并将其财富投资于一个无风险资产和一个风险资产组成的金融市场,其中风险资产的价格过程服从常方差弹性模型.考虑与历史业绩相关的现金流量,保险公司的财富过程由一个时滞随机微分方程刻画,在负指数效用最大化的目标下求解了时滞最优投资与再保险控制问题,分别在投资与再保险和纯投资两种情形下得到最优策略和值函数的解析表达式.最后通过数值算例进一步说明主要参数对最优策略和值函数的影响.     

A projected gradient dynamical system modelling the dynamics of bargaining

We propose a projected gradient dynamical system as a model for a bargaining scheme for an asset for which the two interested agents have personal valuations that do not initially coincide. The personal valuations are formed using subjective beliefs concerning the future states of the world, and the reservation prices are calculated using expected utility theory. The agents are not rigid concerning their subjective probabilities and are willing to update them under the pressure to reach finally an agreement concerning the asset. The proposed projected dynamical system, on the space of probability measures, provides a model for the evolution of the agents, beliefs during the bargaining period and is constructed so that an agreement is reached under the minimum possible deviation of both agents from their initial beliefs. The convergence results are shown using techniques from convex dynamics and Lyapunov function theory.     

OPTIMAL INVESTMENT IN THE PROTECTION OF A VULNERABLE BIOLOGICAL RESOURCE

It is assumed that the probability of destruction of a biological asset by natural hazards can be reduced through investment in protection. Specifically a model, in which the hazard rate depends on both the age of the asset and the accumulated invested protection capital, is assumed. The protection capital depreciates through time and its effectiveness in reducing the hazard rate is subject to diminishing returns. It is shown how the investment schedule to maximize the expected net present value of the asset can be determined using the methods of deterministic optimal control, with the survival probability regarded as a state variable. The optimal investment pattern involves “bang-bang-singular” control. A numerical scheme for determining jointly the optimal investment policy and the optimal harvest (or replacement) age is outlined and a numerical example involving forest fire protection is given.