考虑红利支付与提前退休的最优投资组合

研究了在经济代理人通过不可逆退休时间选择来调整劳动时间框架下的最优消费和投资问题,主要考虑风险资产派发红利的情形.运用随机控制方法,求解使得消费-闲暇预期效用最大化的最优策略.最优投资组合及最优退休时刻表明,代理人在为提前退休积累财富的同时,也能最佳享受消费和闲暇所带来的快乐.     

Knight不确定及机制转换环境下带通胀的最优投资问题研究

本文研究了投资者在Knight不确定及机制转换环境下带通胀的最优投资决策问题.利用Ito公式、α-最大最小预期效用偏好模型、随机分析等方法,得出了机制转换环境下利润流的动力学方程,Knight不确定及机制转换条件下考虑通胀因素的投资预期价值公式,利润流临界现值及不同参数对投资的影响.     

Knight不确定及机制转换环境下带通胀的最优投资问题研究

本文研究了投资者在Knight不确定及机制转换环境下带通胀的最优投资决策问题. 利用Itô公式、α-最大最小预期效用偏好模型、随机分析等方法, 得出了机制转换环境下利润流的动力学方程, Knight 不确定及机制转换条件下考虑通胀因素的投资预期价值公式, 利润流临界现值及不同参数对投资的影响.     

模型不确定和极端事件冲击下带通胀的最优投资组合选择问题研究

本文研究了投资者在极端事件冲击下带通胀的最优投资组合选择问题, 其中投资者不仅对损失风险是厌恶的而且对模型不确定也是厌恶的. 投资者在风险资产和无风险资产中进行投资. 首先, 利用Ito公式推导考虑通胀的消费篮子价格动力学方程, 其次由通胀折现的终端财富预期效用最大化, 对含糊厌恶投资者的最优期望效用进行刻画. 利用动态规划原理, 建立最优消费和投资策略所满足的HJB方程. 再次, 利用市场分解的方法解出HJB方程, 获得投资者最优消费和投资策略的显式解. 最后, 通过数值模拟, 分析了含糊厌恶、风险厌恶、跳和通胀因素对投资者最优资产配置策略的影响.     

带消费习惯的最优消费,寿险和投资决策

本文考虑带消费习惯的个体决策者,如何选择最优的消费,寿险和投资支出,以最大化其效用.假设个体在退休之前将自己的财富在一种无风险资产和一种风险资产上进行分配,并进行消费和购买人寿保险,其目标是最大化退休或死亡前的消费、退休时的财富和遗产组成的效用.我们通过动态规划的方法,得到相应的HJB方程,对于CRRA效用类型的个体,得到最优消费、寿险和投资支出的解析解.通过对比有无消费习惯情况下的解析解,可以发现,加入消费习惯后,个体投资支出会下降;个体的最优消费有了一个随时间变化的下界;当个体的相对风险厌恶系数大于1时,最优消费变化的波动率减小,保费支出也会下降.利用我国的相关数据进行数值模拟,我们发现消费习惯越高的个体,前后期消费支出差距越大,保费支出和投资越低;适应能力越强的个体,消费水平越平滑,承受风险的能力也越大,风险投资越多.     

跳扩散最优控制的随机最大值原理及在金融中的应用

讨论了由金融市场中投资组合和消费选择问题引出的一类最优控制问题,投资者的期望效用是常数相对风险厌恶(CRRA)情形.在跳扩散框架下,利用古典变分法得到了一个局部随机最大值原理.结果应用到最优投资组合和消费选择策略问题,得到了状态反馈形式的显式最优解.     

基于再保险和投资的随机微分博弈

本文研究了具有再保险和投资的随机微分博弈.应用线性-二次控制的理论,在指数效用和幂效用下,求得了最优再保险策略、最优投资策略、最优市场策略和值函数的显示解,推广了文[8]的结果.通过本文的研究,当市场出现最坏的情况时,可以指导保险公司选择恰当的再保险和投资策略使自身所获得的财富最大化.     

部分信息下的最优投资消费策略显示解

本文讨论投资者极大化生命期期望消费效用的最优化问题,在较一般情形下,给出了由证券交易价格（部分信息）决定的最优投资消费策略显示解。     

一类终端财富期望效用最大化问题: 通货膨胀情形

本文研究了一类受通货膨胀影响的终端财富期望效用最大化问题.对常数相对风险厌恶(CRRA) 情形的效用函数,用直接构造的方法得到了代理人的显式最优投资策略和最大期望效用,并给出其经济含义. 该思想来自线性二次最优控制问题中的完全平方技术.根据股票价格和通货膨胀率的历史数据,我们用SAS软件估计出模型中参数的近似值,并给出代理人的最优投资策略和最大期望效用.     

考虑投资者过程效用影响的投资组合模型

传统的投资组合模型只考虑投资结果,而未考虑投资过程带来的效用影响。事实上组合投资期间投资者持有的股票价格的每一次波动都牵动着投资者的神经,带来或正或负的效用,影响投资者的投资决策。分析投资者过程效用的影响因素,设计出风险投资者的投资过程效用函数。并假设投资者的总效用函数为过程效用函数和结果效用函数的线性组合,构建考虑投资行为过程效用的投资组合模型,对模型的解进行数值模拟分析。研究结果表明：对损失过于敏感的投资者受过程影响越大,则投资风险资产的资金比例越低,对损失不敏感的投资者受过程影响越大,投资风险资产的资金比例越高。因此,对损失越不敏感且受过程效用影响越严重的投资者,越容易推高市场风险。对模型的投资绩效进行了实证检验,结果发现：受投资者过程效用影响大的投资组合模型在股市持续上涨阶段的投资表现较好,而在股市盘整阶段和持续下跌阶段表现较差。表明受过程效用影响大的投资者会在股市持续上涨时积极入市,在股市持续下跌时迅速退市,从而加剧股市震荡。     

Optimal portfolio, consumption and retirement decision under a preference change

We investigate an optimal portfolio, consumption and retirement decision problem in which an economic agent can determine the discretionary stopping time as a retirement time with constant labor wage and disutility. We allow the preference of the agent to be changed before and after retirement. It is assumed that the agent's coefficient of relative risk aversion becomes higher after retirement. Under a constant relative risk aversion (CRRA) utility function, we obtain the optimal policies in closed-forms using martingale methods and variational inequality methods. We give some numerical results of the optimal policies. We also consider the relation between the level of disutility and the labor wage with the optimal retirement wealth level.     

Optimal consumption-leisure, portfolio and retirement selection based on α-maxmin expected CES utility with ambiguity

This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by ??-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiplepriors utility and the technique of backward stochastic differential equations (BSDEs), we transform the ??-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor??s uncertainty. Our model investigates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flexibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.     

Optimal investment, stochastic labor income and retirement

We address an optimal consumption-investment-retirement problem with stochastic labor income. We study the Merton problem assuming that the agent has to take four different decisions: the retirement date which is irreversible; the labor and the consumption rate and the portfolio decision before retirement. After retirement the agent only chooses the portfolio and the consumption rate. We confirm some classical results and we show that labor, portfolio and retirement decisions interact in a complex way depending on the spanning opportunities.     

An optimal investment,consumption, leisure,and voluntary retirement problem with Cobb–Douglas utility: Dynamic programming approaches

We consider an optimal consumption, leisure, investment, and voluntary retirement problem for an agent with a Cobb–Douglas utility function. Using dynamic programming, we derive closed form solutions for the value function and optimal strategies for consumption, leisure, investment, and retirement.     

Optimal investment, consumption and retirement choice problem with disutility and subsistence consumption constraints

In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.     

保留效用类型依存的委托代理模型

在代理人的保留效用是类型依存的情况下,代理人的租金受外部机会成本的影响.研究表明,代理人努力负效用与成本类型的单调关系,决定了最优契约安排.相比较于非类型依存的情况,代理人都可能得到租金.高类型的租金总大于0,其租金可能仅源于保留效用,也可能受保留效用与努力负效用的综合影响.为激励其努力工作,委托人必须给予该类型代理人更高的支付;另一方面,低类型代理人的努力成本低和保留效用高,总得到比高类型更多的租金.     

Comparison of optimal portfolios with and without subsistence consumption constraints

We present the effects of the subsistence consumption constraints on a portfolio selection problem for an agent who is free to choose when to retire with a constant relative risk aversion (CRRA) utility function. By comparing the previous studies with and without the constraints expressed by the minimum consumption requirement, the changes of a retirement wealth level and the amount of money invested in the risky asset are derived explicitly. As a result, the subsistence constraints always lead to lower retirement wealth level but do not always induce less investment in the risky asset. This implies that even though the agent who has a restriction on consumption retires with lower wealth level, she invests more money near the retirement when her risk aversion lies inside a certain range.     

On Cournot-Nash equilibria with exogenous uncertainty

A large body of literature has accumulated which examines how the optimal solution of an agent maximizing the expectation of a real-valued function, depending on a random parameterp and the agent's behaviorx, reacts to perturbations in the first and second moments ofp. Here, by an approximation valid for small uncertainty, we allow many agents and consider their behavior in a Cournot-Nash equilibrium. We also allowp to depend on the behaviors of the participating agents. We apply the analysis to two models, one of a Cournot oligopoly, the other of a cooperative of individuals where there is uncertainty in the return to communal work.The second and third authors are grateful to the British Council (Academic Links and Interchange Scheme) for financial support.     

Voluntary retirement and portfolio selection: Dynamic programming approaches

I consider a continuous-time optimal consumption and portfolio selection problem with voluntary retirement. When the agent’s utility of consumption and leisure are of Cobb–Douglas form, I use the dynamic programming method to derive the value function and optimal strategies in closed-form. These coincide with the solutions of Farhi and Panageas (2007) [7], who have solved the problem using a martingale method.