不允许卖空限制下跳-扩散模型的均值-方差策略选择

均值-方差投资策略问题一般是在连续模型下研究的,本文建立了跳-扩散模型下的均值-方差投资选择问题,利用动态规划原理和凸分析得到了最优投资策略和有效边界的解析表达式。本文得到的最优投资策略和有效边界均是在不允许卖空限制下的,通过数值例子分析了交易限制对投资策略和有效边界的影响.     

跳-扩散模型下相对收益过程带停时的均值-方差随机控制

针对跳扩散模型下鞅测度不唯一的问题,利用识别定理和Riccati方程研究了跳扩散模型下带停时的均值-方差随机控制问题,得到了相对收益过程最优投资策略的显式解及相应的最优停时,并且给出了在最优停止时间的均值方差有效边界.     

基于相依风险模型框架均值方差准则下的最优时间一致的投资再保险策略问题（英文）

本文研究了在相依风险模型的框架下保险公司的最优投资和再保险问题.在均值方差准则下,利用博弈论的相关理论,求解扩展的HJB方程系统,得到最优时间一致的投资和再保险策略以及相应的最优值函数,并通过数值例子展现模型参数对最优策略的影响。     

扩散风险模型下再保险和投资对红利的影响

对扩散风险模型,研究了比例再保险和投资对红利的影响．在常数边界分红策略下,得到了使得期望贴现红利最大的最优比例再保险和投资策略的显示表达式,并得到最大期望贴现红利的显示表达式．最后,通过数值计算得到了再保险和投资对期望红利的影响,以及最优投资策略与各参数之间的关系．     

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.     

在不允许卖空条件下的最优比例再保险投资

假设保险公司的盈余过程服从一个带扰动项的布朗运动,保险公司可以投资一个无风险资产和n个风险资产,还可以购买比例再保险,并且风险市场是不允许卖空的.本文在均值一方差优化准则下研究保险公司的最优投资一再保策略选择问题,利用LQ随机控制方法求解模型,得到了保险公司的最优组合投资策略的解析和保险公司投资的有效投资边界的解析表达...     

方差保费原则下具有违约风险的均值-方差保险者的时间一致最优投资和再保险问题（英文）

本文研究在均值-方差准则下保险者的最优投资再保险策略问题,其中保险者可以投资到无风险资产,股票和违约债券上,股票服从Heston模型.保险者可以购买比例再保险或者得到新的保险业务,特别地,保险和再保险的保费通过方差保费原则来计算.通过使用博弈论方法,我们分别解决了违约前和违约后的扩展的HJB方程并且得到了相应的时间一致最优投资再保险策略表达式.最后,我们用数值例子来说明模型参数对最优策略的影响.     

期望和残差收益估计不可靠的鲁棒模型

投资优化问题的最优策略会随着输入参数的扰动而出现敏感的变化,针对投资优化问题中出现的随机变量的参数估计不可靠的情况,本文引入不确定集合描述随机收益的有关矩信息,提出了投资优化问题的一个鲁棒性模型,并采用数学规划的理论和方法,给出了该模型的最优策略和有效前沿的解析表示。本方法能够为采用保守策略的、对不确定性厌恶的投资者提供一种最优的投资策略。     

收益序列相关的动态资产-负债管理

以条件期望体现风险资产收益的相关性,建立了资产收益序列相关时资产-负债管理的动态均值-方差模型.采用Li和Ng(2000)的嵌入法,构造了一个具有二次效用函数的辅助问题,利用动态规划方法及原问题与辅助问题最优策略之间的关系,得到了原问题的最优投资组合策略和有效边界.     

随机市场系数条件下不连续股价的M-V投资组合选择

在假定市场系数为随机过程并且股票价格服从跳跃扩散过程的市场条件下应用鞅方法讨论一个M-V模型的最优投资组合选择问题.通过引进凹函数U(x)以及等价鞅测度,应用鞅方法以及贝叶斯定理得到了最优投资策略以及有效边界表达式.     

Optimal Mean-Variance Investment-Reinsurance Strategy for a Dependent Risk Model with Ornstein-Uhlenbeck Process

In this paper, we investigate the optimal investment-reinsurance strategy for an insurer with two dependent classes of insurance business, where the claim number processes are correlated through a common shock. It is assumed that the insurer can invest her wealth into one risk-free asset and multiple risky assets, and meanwhile, the instantaneous rates of investment return are stochastic and follow mean-reverting processes. Based on the theory of linear-quadratic control, we adopt a backward stochastic differential equation (BSDE) approach to solve the mean-variance optimization problem. Explicit expressions for both the efficient strategy and efficient frontier are derived. Finally, numerical examples are presented to illustrate our results.

     

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.     

Optimal asset allocation for a general portfolio of life insurance policies

Asset liability matching remains an important topic in life insurance research. The objective of this paper is to find an optimal asset allocation for a general portfolio of life insurance policies. Using a multi-asset model to investigate the optimal asset allocation of life insurance reserves, this study obtains formulae for the first two moments of the accumulated asset value. These formulae enable the analysis of portfolio problems and a first approximation of optimal investment strategies. This research provides a new perspective for solving both single-period and multiperiod asset allocation problems in application to life insurance policies. The authors obtain an efficient frontier in the case of single-period method; for the multiperiod method, the optimal asset allocation strategies can differ considerably for different portfolio structures.     

借贷利率限制下资产-负债管理问题的均值-方差模型

将负债过程和借款利率限制引入投资组合优化问题中,并建立该问题的均值-方差模型.通过引入拉格朗日函数并应用拉格朗日对偶定理得到一个等价的新的优化模型,然后应用动态规划原理得到了最优投资策略和有效前沿的解析表达式.算例解释了所得结论.     

A Mean-variance Problem in the Constant Elasticity of Variance (CEV) Mo del

In this paper, we focus on a constant elasticity of variance (CEV) model and want to find its optimal strategies for a mean-variance problem under two con-strained controls: reinsurance/new business an...     

Optimal mean–variance investment and reinsurance problem for an insurer with stochastic volatility

This paper considers an optimal investment and reinsurance problem for an insurer under the mean–variance criterion. The stochastic volatility of the stock price is modeled by a Cox-Ingersoll-Ross (CIR) process. By applying a backward stochastic differential equation (BSDE) approach, we obtain a BSDE related to the underlying investment and reinsurance problem. Then solving the BSDE leads to closed-form expressions for both the efficient frontier and the efficient strategy. In the end, numerical examples are presented to analyze the economic behavior of the efficient frontier.     

ͨ������Ӱ���»������΢�ֲ��ĵ������ٱ��պ�Ͷ��

??Under inflation influence, this paper investigate a stochastic differential game with reinsurance and investment. Insurance company chose a strategy to minimizing the variance of the final wealth, and the financial markets as a game ``virtual hand' chosen a probability measure represents the economic ``environment' to maximize the variance of the final wealth. Through this double game between the insurance companies and the financial markets, get optimal portfolio strategies. When investing, we consider inflation, the method of dealing with inflation is: Firstly, the inflation is converted to the risky assets, and then constructs the wealth process. Through change the original based on the mean-variance criteria stochastic differential game into unrestricted cases, then application linear-quadratic control theory obtain optimal reinsurance strategy and investment strategy and optimal market strategy as well as the closed form expression of efficient frontier are obtained; finally get reinsurance strategy and optimal investment strategy and optimal market strategy as well as the closed form expression of efficient frontier for the original stochastic differential game.     

Optimal Mean-Variance Problem with Constrained Controls in a Jump-Diffusion Financial Market for an Insurer

In this paper, we study the optimal investment and optimal reinsurance problem for an insurer under the criterion of mean-variance. The insurer’s risk process is modeled by a compound Poisson process and the insurer can invest in a risk-free asset and a risky asset whose price follows a jump-diffusion process. In addition, the insurer can purchase new business (such as reinsurance). The controls (investment and reinsurance strategies) are constrained to take nonnegative values due to nonnegative new business and no-shorting constraint of the risky asset. We use the stochastic linear-quadratic (LQ) control theory to derive the optimal value and the optimal strategy. The corresponding Hamilton–Jacobi–Bellman (HJB) equation no longer has a classical solution. With the framework of viscosity solution, we give a new verification theorem, and then the efficient strategy (optimal investment strategy and optimal reinsurance strategy) and the efficient frontier are derived explicitly.     

Mean–variance asset–liability management with asset correlation risk and insurance liabilities

Consider an insurer who invests in the financial market where correlations among risky asset returns are randomly changing over time. The insurer who faces the risk of paying stochastic insurance claims needs to manage her asset and liability by taking into account of the correlation risk. This paper investigates the impact of correlation risk to the optimal asset–liability management (ALM) of an insurer. We employ the Wishart process to model the stochastic covariance matrix of risky asset returns. The insurer aims to minimize the variance of the terminal wealth given an expected terminal wealth subject to the risk of paying out random liabilities of compound Poisson process. This ALM problem then becomes a linear–quadratic stochastic optimal control problem with stochastic volatilities, stochastic correlations and jumps. The recognition of an affine form in the solution process enables us to derive the explicit closed-form solution to the optimal ALM portfolio policy, obtain the efficient frontier, and identify the condition that the solution is well behaved.     

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.