风险内生的委托代理模型研究

证券投资基金的委托代理关系与一般的委托代理关系不同,在一般的委托代理关系中,产出的风险是外生的,而基金产出的风险是内生的,即风险是由基金管理人来选择的.在模型假设的背景下,在不考虑基金管理人的努力成本时,基金委托代理关系中不存在道德风险问题.如果考虑基金管理人的努力成本,当其行为不可观测时,基金投资者无法通过契约参数的变化来影响基金管理人的努力水平,但此时投资组合的风险水平将低于基金管理人行为可观测时的情况.实证研究证实了基金收益分享比例与基金管理人努力程度无关的模型推论.     

赎回风险约束的开放式基金管理费研究

从赎回风险的视角研究开放式基金的管理费.以赎回风险为内生变量构建了基金管理人的动态投资决策模型,利用动态优化的Bellman原理得到了最优管理费.进一步分析发现:一是基金管理费与基金管理人的投资能力正相关,即基金管理人的投资能力越强,收取的基金管理费越多;二是基金管理费与投资者的赎回率负相关,即投资者的赎回率越大,基金管理费越少.而且选取中国股票型开放式基金的数据构建VAR计量经济模型,检验基金管理人的投资能力与投资者的赎回风险对基金管理费的影响,实证结果支持理论模型的结论.     

最优分红策略:正则与脉冲混合控制问题

本文对扩散模型下的最优分红问题作了进一步分析.注意到,累积分红量是一个关于时间的右连左极过程,它的路径由连续和跳跃两部分组成.因此,本文在建模中同时加入了连续分红和脉冲分红两种形式,这就构成了一个正则和脉冲分红混合的最优控制问题.假设所有分红量存在一个比例成本,对于每次的脉冲分红量存在一个固定成本.此外,对于连续分红部分,假设存在一个有限的最大分红率.用漂移Brown运动描述公司的盈余过程,优化目标设定为最大化公司破产前分红现值的期望值,本文给出了值函数以及最优分红策略的解析表达式.结论表明,最优的分红策略为阀值(threshold)策略和脉冲策略的组合形式.     

私募基金规模、申购赎回机制与动态道德风险

运用动态合约理论与实物期权理论研究了私募基金最优激励相容合约的一般特征,考察了基金规模与申购赎回机制对缓解道德风险的作用。结论表明,私募基金最优激励相容合约由投资人的最大预期收益与管理者的最大预期回报共同决定,且购买私募基金类似于做多一种特殊期权,该期权标的资产价格由管理者后续值度量;投资人为激励管理者努力工作而付出的激励成本随基金初始规模或再申购比例递增,而最优基金规模由其边际激励成本与预期边际业绩决定;赎回成本影响投资人的最大预期收益,但对缓解道德风险不具显著作用;适当的业绩抽成可降低道德风险,且业绩抽成与私募基金初始规模或再申购比例在缓解道德风险方面存在一定的替代性。     

脉冲和正则控制下的最优注资:一种混合策略

本文用漂移Brown运动表示公司的现金流,研究了公司的最优注资问题.基于实际情况,本文假设市场上有两种注资类型:脉冲注资和正则注资,同时假设这两种注资都需要支付比例成本,且每次脉冲注资还需支付固定成本.公司决策者要确定公司的注资策略,就需要确定正则注资率(有最大值限制)、注资的时间和脉冲注资量.从控制公司成本的角度出发,决策者需在现金流为正的约束下,寻找最小化注资成本的注资策略.因此,决策者面临一个脉冲和正则控制的混合问题,本文得到了该问题的值函数和最优控制策略,发现最优的注资策略是与模型参数相关的混合注资策略,同时也分析了模型参数对值函数和最优注资策略的敏感性.     

微生物批式流加发酵脉冲系统的参数辨识及稳定性

针对微生物批式流加发酵生产1,3-丙二醇的非线性脉冲系统,建立敏感参数的优化辨识模型(PDP),论述了模型解的性质、解与参量的关系以及辨识问题最优解的存在性.通过构造算法求得辨识问题最优解,并讨论了新参数下脉冲系统解的稳定性.     

具有脉冲扩散的近远海渔业系统的周期优化收获策略

研究了一类在周期环境中具有脉冲扩散及收获的近远海渔业系统的动力学行为和优化控制问题.系统中近远海鱼群每隔一定时间进行一次迁移扩散,为了经济利益对近海鱼群进行比例收获.在系统保持周期变化的条件下,选择收获努力量为控制变量,考虑收获成本因素,以一个周期内经济净收益最大为目标研究最优收获策略.首先研究了收获系统周期解的存在性和稳定性,并利用脉冲微分系统的极值原理获得了周期优化控制策略的具体表达式.     

二阶非线性混合型脉冲积微分方程和最优控制

本文研究Banach空间中受无界算子扰动的二阶非线性混合型脉冲积微分方程.构造无界算子矩阵生成的半群,合理引进方程的PC-温和解并证明其存在性.讨论阶非线性混合型脉冲积微分方程所决定的一类Lagrange问题,给出了最优对存在的充分条件.-个例子展示了所得结果的应用.     

证券投资基金管理人选择中的信号传递博弈

本文通过对证券投资基金这种资金运作方式的分析和研究,结合信号传递博弈模型,提出一种对资金管理人投资能力的评估方法.主要分析基金管理人的努力成本对最后投资能力评估结果的影响,为投资人选择基金管理人提供新的思路,也为基金管理人争取融资成功提供一定的帮助.     

基于Stein-Stein波动率和动态VaR约束下DC型养老基金的最优投资策略

研究了确定缴费型养老基金在退休前累积阶段的最优资产配置问题.假设养老基金管理者将养老基金投资于由一个无风险资产和一个价格过程满足Stein-Stein随机波动率模型的风险资产所构成的金融市场.利用随机最优控制方法,以最大化退休时刻养老基金账户相对财富的期望效用为目标,分别获得了无约束情形和受动态VaR (Value at Risk)约束情形下该养老基金的最优投资策略,并获得相应最优值函数的解析表达形式.最后通过数值算例对相关理论结果进行数值验证并考察了最优投资策略关于相关参数的敏感性.     

基于Copula的开放式基金流动性风险研究

从基金管理者的角度出发,引入了一种开放式基金预留现金和债券比例管理模型,它可以使满足及时赎回需求概率很大且预留现金和债券最少.使用二元Archimedean Copula分析了预留现金和债券比例的计算公式,通过数值实例分析了预留比例公式的合理性,为基金管理人制定投资目标时随时控制预留现金的比例,提供一个参考的标准.     

超额控制权与企业现金持有——基于家族创始人控制的调节效应

本文基于代理成本理论、动态权衡理论,选取2007年~2017年中国沪、深A 股家族上市公司数据,实证检验了家族企业超额控制权对现金持有水平的内在影响。研究结论显示:(1)家族超额控制权与现金持有水平显著正相关;(2)而家族创始人控制能够有效的抑制家族超额控制权对现金持有水平的影响。在控制了超额控制权的影响之后,进一步研究发现:(3)与非创始控制家族相比,创始家族的现金持有水平显著低于非创始家族。本文的研究结论不仅在微观治理层面,进一步证实了家族超额控制的“寻租观”,与此同时也揭示出,创始人在家族企业公司治理中所扮演的积极角色。     

The optimal order and payment policies for deteriorating items in discount cash flows analysis under the alternatives of conditionally permissible delay in payments and cash discount

This study investigates a deteriorating inventory problem in which the supplier simultaneously offers the retailer either a conditionally permissible delay in payments or a cash discount. In the case of a conditionally permissible delay, if the retailer orders more than a predetermined quantity, then he/she has a grace period to make the full payment. Otherwise, he/she must pay the payment for goods of certain proportion first while receiving the goods and has a grace period to pay off the rest. As to a cash discount, if the retailer pays for the entire amount of the order within a certain short period, then he/she will receive a cash discount from the supplier. In additions, from a financial standpoint, all cash outflows related to the inventory control that occur at different points of time have different values. Hence, it is necessary to take account of the factor of time value of monetary when drafting the replenishment policy. In a word, this paper uses an alternate approach-discount cash flow (DCF) analysis to establish an inventory problem for deteriorating items in which the supplier provides the retailer either a conditionally permissible delay or a cash discount. We then study the necessary and sufficient conditions for finding the optimal solution. Furthermore, we establish several theoretical results to obtain the solution that provides the smallest present value of all future cash flows. Finally, several numerical examples are given to illustrate the results and obtain some managerial insights.     

Analysis of the stochastic cash balance problem using a level crossing technique

The simple cash management problem includes the following considerations: the opportunity cost of holding too much cash versus the penalty cost of not having enough cash to meet current needs; the cost incurred (or profit generated) when making changes to cash levels by increasing or decreasing them when necessary; the uncertainty in timing and magnitude of cash receipts and cash disbursements; and the type of control policy that should be used to minimize the required level of cash balances and related costs. In this paper, we study a version of this problem in which cash receipts and cash disbursements occur according to two independent compound Poisson processes. The cash balance is monitored continuously and an order-point, order-up-to-level, and keep-level \( \left( {s, S, M} \right) \) policy is used to monitor the content, where \( s \le S \le M \). That is, (a) if, at any time, the cash level is below s, an order is immediately placed to raise the level to S; (b) if the cash level is between s and M, no action is taken; (c) if the cash level is greater than M, the amount in excess of M is placed into an earning asset. We seek to minimize the expected total costs per unit time of running the cash balance. We use a level-crossing approach to develop a solution procedure for finding the optimal policy parameters and costs. Several numerical examples are given to illustrate the tradeoffs.     

基于随机活动工期的多模式现金流均衡项目调度优化

承包商在项目执行过程中的现金流均衡是保证项目成功的关键因素。本文研究基于随机活动工期的多模式现金流均衡项目调度问题,旨是在项目工期及鲁棒性阈值约束下合理安排活动执行模式与开始时间,实现承包商现金流均衡。本文通过构建整数规划优化模型对研究问题进行刻画,随后设计模拟退火算法进行求解,最后进行案例分析。结果表明:鲁棒性阈值虽然可以保证基准进度的稳定性,但是提高鲁棒性阈值水平反而不利于承包商的现金流均衡,该值过高时甚至得不到可行解。本文研究可为随机活动工期背景下承包商的现金流控制提供定量化决策支持。     

现金持有动态调整机制——基于动态面板模型的实证分析

本文通过建立动态面板数据模型,系统地研究了中国企业现金持有的动态调整机制。发现:第一,企业存在最优目标现金持有水平,现金持有策略倾向于围绕这一目标进行动态调整,但是我国资本市场动态调整的成本较高;第二,现金持有不足企业的调整速度快于超额现金持有企业的调整速度,这说明,相对于超额现金持有带来的代理成本负面影响,企业更加倾向于关注现金持有不足所产生的流动性短缺风险。并且统计过程表明系统广义矩方法在动态面板模型估计中具有合理性。     

Classical and singular stochastic control for the optimal dividend policy when there is regime switching

Motivated by economic and empirical arguments, we consider a company whose cash surplus is affected by macroeconomic conditions. Specifically, we model the cash surplus as a Brownian motion with drift and volatility modulated by an observable continuous-time Markov chain that represents the regime of the economy. The objective of the management is to select the dividend policy that maximizes the expected total discounted dividend payments to be received by the shareholders. We study two different cases: bounded dividend rates and unbounded dividend rates. These cases generate, respectively, problems of classical stochastic control with regime switching and singular stochastic control with regime switching. We solve these problems, and obtain the first analytical solutions for the optimal dividend policy in the presence of business cycles. We prove that the optimal dividend policy depends strongly on macroeconomic conditions.     

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For a financial or insurance entity, the problem of finding the optimal dividend distribution strategy and optimal firm value function is a widely discussed topic. In the present paper, it is assumed that the firm faces two types of liquidity risks: a Brownian risk and a Poisson risk. The firm can control the time and amount of dividends paid out to shareholders. By sufficiently taking into account the safety of the company, bankruptcy is said to take place at time $t$ if the cash reserve of the firm runs below the linear barrier b+kt (not zero), see 1. We deal with the problem of maximizing the expected total discounted dividends paid out until bankruptcy. The optimal dividend return (or, firm value) function is identified as the classical solution of the associated Hamilton-Jacobi-Bellman (HJB) equation where a second-order differential-integro equation is involved. By solving the corresponding HJB equation, the analytical solution of the optimal firm value function is obtained, the optimal dividend strategy is also characterized, which is of linear barrier type: at time t the firm keeps cash inside when the cash reserves level is less than a critical linear barrier and pays cash in excess of this linear barrier as dividends.     

Optimal cash management using impulse control

We consider the impulse control of Lévy processes under the infinite horizon, discounted cost criterion. Our motivating example is the cash management problem in which a controller is charged a fixed plus proportional cost for adding to or withdrawing from his/her reserve, plus an opportunity cost for keeping any cash on hand. Our main result is to provide a verification theorem for the optimality of control band policies in this scenario. We also analyze the transient and steady-state behavior of the controlled process under control band policies and explicitly solve for an optimal policy in the case in which the Lévy process to be controlled is the sum of a Brownian motion with drift and a compound Poisson process with exponentially distributed jump sizes.     

A unified treatment of dividend payment problems under fixed cost and implementation delays

In this paper we study the dividend optimization problem for a corporation or a financial institution when the management faces (regulatory) implementation delays. We consider several cash reservoir models for the firm including two mean-reverting processes, Ornstein–Uhlenbeck and square-root processes. Since the cash flow structure of different companies have different qualitative behaviors, it makes sense to use different diffusions to model them. The delay causes significant difficulties to the optimization problem since the cash reservoir fluctuates during the delay period. We provide a uniform mathematical framework to analyze all the models and provide optimal threshold strategies at which the management initiates actions, i.e., declaration and payment of dividends. Our solution depends on a new characterization of the value function for one-dimensional diffusions and provide easily implementable algorithms to find the optimal control and the value function.