均值-方差准则下具有负债的随机微分博弈

研究了均值-方差准则下,具有负债的随机微分博弈.研究目标是:在终值财富的均值等于k的限制下,在市场出现最坏的情况下找到最优的投资策略使终值财富的方差最小.即:基于均值-方差随机微分博弈的投资组合选择问题.使用线性-二次控制的理论解决了该问题,获得了最优的投资策略、最优市场策略和有效边界的显示解.并通过对所得结果进行进一步分析,在经济上给出了进一步的解释.通过本文的研究,可以指导金融公司在面临负债和金融市场情况恶劣时,选择恰当的投资策略使自身获得一定的财富而面临的风险最小.     

通货膨胀影响下基于随机微分博弈的最优再保险和投资

本文在通货膨胀影响下,研究了具有再保险和投资的随机微分博弈.保险公司选择一个策略最小化终值财富的方差,而金融市场作为博弈的"虚拟手"选择一个概率测度所代表的经济"环境"最大化保险公司考虑的最小化终值财富的方差.通过保险公司和金融市场之间的这种双重博弈得到最优的投资组合.进行投资时考虑了通货膨胀的影响,通货膨胀的处理方式为:首先考虑通货膨胀对风险资产进行折算,然后再构造财富过程.通过把原先的基于均值-方差准则的随机微分博弈转化为无限制情况,应用线性-二次控制理论得到了无限制情况下最优再保险、投资、市场策略和有效边界的显式解;进而得到了原基于均值-方差准则的随机微分博弈的最优再保险、投资、市场策略和有效边界的显式解.     

均值-方差准则下CEV模型的最优投资和再保险

研究了经典Cramer-Lundberg风险模型的均值-方差策略选择问题.保险公司可以采取再保险和在金融市场上投资来减小风险和增加财富.风险资产的价格通过CEV模型来描述,它是Black-Scholes模型的推广.通过把原先的均值-方差问题转化为一个辅助问题,应用线性-二次控制理论解决了辅助问题.最终获得了最优的再保险、投资策略和有效边界的显式解,同时得到了最小终值方差和相应的策略.     

跳扩散市场投资组合研究

研究了连续时间动态均值-方差投资组合选择问题.假设风险资产价格服从跳跃-扩散过程且具有卖空约束.投资者的目标是在给定期望终止时刻财富条件下,最小化终止时刻财富的方差.通过求解模型相应的Hamilton-Jacobi-Bellmen方程,得到了最优投资策略及有效前沿的显示解.结果显示,风险资产的卖空约束及价格过程的跳跃因素对最优投资策略及有效前沿的是不可忽略的.     

带负债的连续时间最优资产组合选择

构造了一个带外生负债的连续时间均值-方差最优投资组合选择模型.假定风险资产价格的演变服从几何布朗运动,累积负债服从带漂移的布朗运动,并且市场系数恒为常数,借助随机LQ控制方法得到相应的均值-方差优化问题的最优策略和有效边界.     

风险资产价格服从CEV模型的投资组合随机微分博弈

本文在风险资产价格服从CEV模型时,讨论两个投资者的时间一致均值-方差最优投资组合选择的随机微分博弈问题.运用动态规划原理,求得了最优投资策略及相应的值函数.     

基于通货膨胀风险和Heston随机波动率下的最优资产配置

本文考虑了基于均值-方差准则下的连续时间投资组合选择问题。为了对冲市场中的利率风险和通货膨胀风险,假定市场上存在可供交易的零息名义债券和零息通货膨胀指数债券。另外,投资者还可以投资一个价格具有Heston随机波动率的风险资产。首先建立了基于均值-方差框架下的最优投资组合问题,然后将原问题进行转换,利用随机动态规划方法和对偶Lagrangian原理,获得了均值-方差准则下的有效投资策略以及有效前沿的解析表达形式,最后对相关参数的敏感性进行了分析。     

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.     

含有信用风险的跳扩散市场的最优组合选择

假定投资者将其财富分配在这样两种风险资产中,一种是股票,价格服从跳跃扩散过程;一种是有信用风险的债券,其价格服从复合泊松过程.在均值-方差准则下通过最优控制原理来研究投资者的最优投资策略选择问题,得到了最优投资策略及有效边界,最后通过数值例子分析了违约强度、债券预期收益率以及目标财富对最优投资策略的影响.     

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.     

跳扩散模型下的非零和随机微分投资组合博弈

现实经济中,当股票价格受到一些重大信息影响而发生突发性的跳跃时,用跳扩散过程来描述股票价格的趋势更符合实际情况。基于这一观察,本文研究跳扩散模型下包含两个投资者的非零和投资组合博弈问题。假设金融市场中包含一种无风险资产和一种风险资产,其中风险资产的价格动态用跳扩散模型来描述。将该非零和博弈问题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端时刻自身财富与其竞争对手财富差的均值-方差效用。运用随机控制理论,得到了均衡投资策略以及相应值函数的解析表达。最后通过数值仿真算例分析了模型相关参数变动对均衡投资策略的影响。仿真结果显示:当股价发生不连续跳跃,投资者在构造投资策略时考虑跳跃风险可以显著增加其效用水平;同时,随着博弈竞争的加剧,投资者为了在竞争中取得更好的表现,往往会采取更加激进的投资策略,增加对风险资产的投资。     

Mean-variance portfolio selection for a non-life insurance company

We consider a collective insurance risk model with a compound Cox claim process, in which the evolution of a claim intensity is described by a stochastic differential equation driven by a Brownian motion. The insurer operates in a financial market consisting of a risk-free asset with a constant force of interest and a risky asset which price is driven by a Lévy noise. We investigate two optimization problems. The first one is the classical mean-variance portfolio selection. In this case the efficient frontier is derived. The second optimization problem, except the mean-variance terminal objective, includes also a running cost penalizing deviations of the insurer’s wealth from a specified profit-solvency target which is a random process. In order to find optimal strategies we apply techniques from the stochastic control theory.     

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.     

Classical mean-variance model revisited: pseudo efficiency

Investigating the inverse problem of the classical Markowitz mean-variance formulation: Given a mean-variance pair, find initial investment levels and their corresponding portfolio policies such that the given mean-variance pair can be realized, we reveal that any mean-variance pair inside the reachable region can be achieved by multiple portfolio policies associated with different initial investment levels. Therefore, in the mean-variance world for a market of all risky assets, the common belief of monotonicity: ‘The larger you invest, the larger expected future wealth you can expect for a given risk (variance) level’ does not hold, which stimulates us to extend the classical two-objective mean-variance framework to an expanded three-objective framework: to maximize the mean and minimize the variance of the final wealth as well as to minimize the initial investment level. As a result, we eliminate from the policy candidate list the set of pseudo efficient policies that are efficient in the original mean-variance space, but inefficient in this newly introduced three-dimensional objective space.     

The efficient frontier for bounded assets

This paper develops a closed form solution of the mean-variance portfolio selection problem for uncorrelated and bounded assets when an additional technical assumption is satisfied. Although the assumption of uncorrelated assets is unduly restrictive, the explicit determination of the efficient asset holdings in the presence of bound constraints gives insight into the nature of the efficient frontier. The mean-variance portfolio selection problem considered here deals with the budget constraint and lower bounds or the budget constraint and upper bounds. For the mean-variance portfolio selection problem dealing with lower bounds the closed form solution is derived for two cases: a universe of only risky assets and a universe of risky assets plus an additional asset which is risk free. For the mean-variance portfolio selection problem dealing with upper bounds, the results presented are for a universe consisting only of risky assets. In each case, the order in which the assets are driven to their bounds depends on the ordering of their expected returns.     

Robust Optimal Investment Problem with Delay under Heston’s Model

This paper considers a robust optimal portfolio problem under Heston model in which the risky asset price is related to the historical performance. The finance market includes a riskless asset and a risky asset whose price is controlled by a stochastic delay equation. The objective is to choose the investment strategy to maximize the minimal expected utility of terminal wealth. By employing dynamic programming principle and Hamilton-Jacobin-Bellman (HJB) equation, we obtain the specific expression of the optimal control and the explicit solution of the corresponding HJB equation. Besides, a verification theorem is provided to ensure the value function is indeed the solution of the HJB equation. Finally, we use numerical examples to illustrate the relationship between the optimal strategy and parameters.

     

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??In this paper, we investigate a robust optimal portfolio and reinsurance problem under inflation risk for an ambiguity-averse insurer (AAI), who worries about uncertainty in model parameters. We assume that the AAI is allowed to purchase proportional reinsurance and invest his/her wealth in a financial market which consists of a risk-free asset and a risky asset. The objective of the AAI is to maximize the minimal expected power utility of terminal wealth. By using techniques of stochastic control theory, closed-form expressions for the value function and optimal strategies are obtained.