部分信息情形下带有红利的最优投资模型研究

本文讨论部分信息情形下带有红利的最优投资策略,推广了Lakner模型.     

带有交易成本和红利的最优消费投资策略研究

本文利用HJB方程粘性解理论,考虑带有红利收益和交易成本后,对现有最优消费投资模型作了推广,研究了投资者在带有红利和交易成本情形下的最优消费投资策略。     

部分信息下股票付息的Black-Scholes期权定价公式和一类最优投资问题

假定金融市场中的投资者仅掌握部分信息,即投资者仅能观测到股票和债券价格,而股票的瞬时回报率和市场的噪声源不能观测.对存款利率和贷款利率不相等的情形,运用凸分析和滤波技术得到了部分信息下股票付红利的Black-Scholes期权定价公式.对部分信息下最大化终端财富的问题,获得了最优投资策略.     

部分信息下带有保费返还条款的DC养老金时间一致性投资策略

本文研究了部分信息下带有保费返还条款的DC养老金的时间一致性投资策略.假设养老金管理者只拥有股票的部分信息,即只能观测到股票的价格,而不能观测到股票的收益率.养老金带有保费返还条款,在基金累积期死亡的参与者可以获得前期缴纳的所有保费.此外,本文还考虑了通胀风险以及随机工资.首先,利用卡尔曼滤波理论,将部分信息情形下的最优投资组合问题转化为一个完全信息情形下的问题.然后,通过求解一个扩展的HJB方程,得到时间一致性投资策略和最优值函数,并给出了均值–方差有效前沿的参数表达式.最后,用蒙特卡洛方法进行数值模拟,分析了部分信息和保费返还条款对股票投资比例和有效前沿的影响,并给出了相应的经济学解释.     

不同风险度量约束下带有红利的投资组合模型研究

对现有的在风险度量约束下的投资组合模型进行了推广.建立了带有红利情形的随机股票市场模型,给出了投资组合关于这些风险度量约束下的最优化结果.     

奈特不确定下考虑红利和机制转换的最优消费投资

分析了在奈特不确定性环境下,股票的预期回报率服从Markov链的跨期消费和资产选择问题.首先,对由风险资产预期回报构成的不可观测状态下的隐Marbv状态转换模型做出了刻画,使人们对感性的“不可观测状态”的实际金融市场到其精确的数学模型表达有一个清晰的认识.其次,在连续时间风险模型下,假设具有递归多先验效用的投资者拥有一个不可观测的投资机会的先验集,借助Malliavin导数和随机积分方程求解投资者最优消费和投资策略的显式表达式.通过数值模拟分析时,发现不完备信息下的连续Bayes修正产生了能够削减跨期对冲需求的含糊对冲需求,含糊厌恶增大了最优投资组合策略中对冲需求的重要性.讨论了当市场上出现红利因素,上述最优投资组合结论将会发生何种变化,并对红利因素进行具体的量化,定量地研究不同大小的红利对最优投资组合的影响.最后,利用Monte Carlo Malliavin导数模拟计算法分别说明了考虑含糊情形下最优股票需求和跨期对冲需求的变化趋势,且考虑在股票是否考虑支付红利的情况下对投资的影响.     

Omega模型下带投资的红利策略研究

本文在Omega模型下研究一种带投资的分红策略,即当盈余超过边界k时,用部分超额收益作为红利直接分发,另一部分则作为投资资本进行多阶段动态投资,在特定时刻将所得收益与投资成本之和作为红利进行分发.本文在此分红策略下,最终得到最优动态投资策略以及最优红利策略.     

部分信息情形下利率非零时的最优消费投资模型研究

考虑了部分信息情形下市场利率非零时的最优消费投资模型,讨论了相应的最优消费投资策略.最后探讨了当扩散系数可逆且漂移系数服从已知分布时的贝叶斯特例,给出了最优交易策略的明确表达式.     

部分信息下期望消费效用最大的优化问题

研究了部分信息下期望消费效用最大的优化问题.利用凸分析理论,非线性滤波和Malliavin导数技术,得到了最优投资-消费策略和代价泛函.对于对数效用函数情形,给出了一个估算信息价值的公式,它是完全信息下和部分信息下所对应的最优代价泛函的差值.     

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.     

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This paper considers a dividend strategy with investment in Omega model. If at a potential dividend-payment time the surplus is above, part of the excess are paid as dividends directly, the other part are used as dynamic investment capital, at a particular time, the sum of profits and investment capital will be paid as another dividend. Under this dividend policy, we get the optimal dividend strategy and the optimal portfolio policy.     

Portfolio optimization with early announced discrete dividends

In this article we include discrete dividends in the stock price model and solve the corresponding generalized portfolio optimization problem. For this, we develop a new discrete dividend model that allows for the possibility of early announcement and ensures that the drop of the stock price at the ex-dividend date equals the dividend. The resulting portfolio problem can be solved explicitly for both the wealth and the trading strategy. We find that the resulting optimal portfolio process differs from the Merton strategy.     

基于隐Markov模型的最优资产组合选择

在具有可观测和不可观测状态的金融市场中,利用隐马尔可夫链描述不可观测状态的动态过程,研究了不完全信息市场中的多阶段最优投资组合选择问题.通过构造充分统计量,不完全信息下的投资组合优化问题转化为完全信息下的投资组合优化问题,利用动态规划方法求得了最优投资组合策略和最优值函数的解析解.作为特例,还给出了市场状态完全可观测时的最优投资组合策略和最优值函数.     

Time-consistent investment strategy under partial information

This paper considers a mean–variance portfolio selection problem under partial information, that is, the investor can observe the risky asset price with random drift which is not directly observable in financial markets. Since the dynamic mean–variance portfolio selection problem is time inconsistent, to seek the time-consistent investment strategy, the optimization problem is formulated and tackled in a game theoretic framework. Closed-form expressions of the equilibrium investment strategy and the corresponding equilibrium value function under partial information are derived by solving an extended Hamilton–Jacobi–Bellman system of equations. In addition, the results are also given under complete information, which are need for the partial information case. Furthermore, some numerical examples are presented to illustrate the derived equilibrium investment strategies and numerical sensitivity analysis is provided.     

连续时间证券组合安全第一准则

马科维茨均值-方差分析是研究证券组合选择的一种基本方法,而Roy提出一种＂安全第一＂准则,该准则多出现在单阶段与多阶段证券组合选择的研究中.本文分别在完全信息与部分信息下,运用安全第一准则分别研究了连续时间证券组合选择问题,利用鞅方法与Malliavin分析得到投资者的最优投资策略.     

On the Bail-Out Optimal Dividend Problem

This paper studies the optimal dividend problem with capital injection under the constraint that the cumulative dividend strategy is absolutely continuous. We consider an open problem of the general spectrally negative case and derive the optimal solution explicitly using the fluctuation identities of the refracted–reflected Lévy process. The optimal strategy as well as the value function is concisely written in terms of the scale function. Numerical results are also provided to confirm the analytical conclusions.     

Dividend maximization under consideration of the time value of ruin

In the Cramér-Lundberg model and its diffusion approximation, it is a classical problem to find the optimal dividend payment strategy that maximizes the expected value of the discounted dividend payments until ruin. One often raised disadvantage of this approach is the fact that such a strategy does not take the lifetime of the controlled process into account. In this paper we introduce a value function which considers both expected dividends and the time value of ruin. For both the diffusion model and the Cramér-Lundberg model with exponential claim sizes, the problem is solved and in either case the optimal strategy is identified, which for unbounded dividend intensity is a barrier strategy and for bounded dividend intensity is of threshold type.     

Necessary and Sufficient Optimality Conditions for Regular–Singular Stochastic Differential Games with Asymmetric Information

We consider a class of regular–singular stochastic differential games arising in the optimal investment and dividend problem of an insurer under model uncertainty. The information available to the two players is asymmetric partial information and the control variable of each player consists of two components: regular control and singular control. We establish the necessary and sufficient optimality conditions for the saddle point of the zero-sum game. Then, as an application, these conditions are applied to an optimal investment and dividend problem of an insurer under model uncertainty. Furthermore, we generalize our results to the nonzero-sum regular–singular game with asymmetric information, and then the Nash equilibrium point is characterized.     

Multi‐period mean variance portfolio selection under incomplete information

This paper solves an optimal portfolio selection problem in the discrete‐time setting where the states of the financial market cannot be completely observed, which breaks the common assumption that the states of the financial market are fully observable. The dynamics of the unobservable market state is formulated by a hidden Markov chain, and the return of the risky asset is modulated by the unobservable market state. Based on the observed information up to the decision moment, an investor wants to find the optimal multi‐period investment strategy to maximize the mean‐variance utility of the terminal wealth. By adopting a sufficient statistic, the portfolio optimization problem with incompletely observable information is converted into the one with completely observable information. The optimal investment strategy is derived by using the dynamic programming approach and the embedding technique, and the efficient frontier is also presented. Compared with the case when the market state can be completely observed, we find that the unobservable market state does decrease the investment value on the risky asset in average. Finally, numerical results illustrate the impact of the unobservable market state on the efficient frontier, the optimal investment strategy and the Sharpe ratio. Copyright © 2016 John Wiley & Sons, Ltd.