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1.
研究了两个风险厌恶的竞争的机构投资者之间的离散时间最优投资选择博弈模型,每个机构投资者都考虑其竞争对手的相对业绩.机构投资者可以投资于相同的无风险资产和不同的具有相关关系的风险股票,以反映投资的资产专门化.机构投资者选择动态投资策略使得终端绝对财富和相对财富的加权和的期望效用最大.首先,定义了Nash均衡投资策略.其次,在资产专门化和机构投资者具有指数效用函数下,得到了Nash均衡投资策略和值函数的显示表达式,分析了机构投资者之间的竞争对Nash均衡投资策略和值函数的影响.然后,在资产分散化和股票的收益率服从正态分布下,得到了Nash均衡投资策略和值函数的显示表达式,给出了Nash均衡投资策略和值函数与模型主要参数之间的关系.最后,通过数值计算给出了机构投资者采取专门化投资策略,还是分散化投资策略的条件.结果表明机构投资者之间的竞争会影响其对风险的承担,投资机会集对机构投资者的Nash均衡投资策略和值函数会产生很大的影响.  相似文献   

2.
本文研究基于随机基准的最优投资组合选择问题. 假设投资者可以投资于一种无风险资产和一种风险股票,并且选择某一基准作为目标. 基准是随机的, 并且与风险股票相关. 投资者选择最优的投资组合策略使得终端期望绝对财富和基于基准的相对财富效用最大. 首先, 利用动态规划原理建立相应的HJB方程, 并在幂效用函数下,得到最优投资组合策略和值函数的显示表达式. 然后,分析相对业绩对投资者最优投资组合策略和值函数的影响. 最后, 通过数值计算给出了最优投资组合策略和效用损益与模型主要参数之间的关系.  相似文献   

3.
朱怀念  朱莹 《运筹与管理》2021,30(10):183-190
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。  相似文献   

4.
建立了Cox-Ingersoll-Ross随机利率下的关于两个投资者的投资组合效用微分博弈模型.市场利率具有CIR动力,博弈双方存在唯一的损益函数,损益函数取决于投资者的投资组合财富.一方选择动态投资组合策略以最大化损益函数,而另一方则最小化损益函数.运用随机控制理论,在一般的效用函数下得到了基于效用的博弈双方的最优策略.特别考虑了常数相对风险厌恶情形,获得了显示的最优投资组合策略和博弈值.最后给出了数值例子和仿真结果以说明本文的结论.  相似文献   

5.
在考虑时滞效应的影响下研究了非零和随机微分投资与再保险博弈问题。以最大化终端绝对财富和相对财富的均值-方差效用为目标,构建了两个相互竞争的保险公司之间的非零和投资与再保险博弈模型,分别在经典风险模型和近似扩散风险模型下探讨了博弈的Nash均衡策略。借助随机控制理论以及相应的广义Hamilton-Jacobi-Bellman(HJB)方程,得到了均衡投资与再保险策略和值函数的显式表达。最后,通过数值例子分析了模型中相关参数变动对均衡策略的影响。  相似文献   

6.
本文研究了Heston随机波动模型下两个投资人之间的随机微分投资组合博弈问题。假设金融市场上存在价格过程服从常微分方程的无风险资产和价格过程服从Heston随机波动率模型的风险资产。该博弈问题被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止时刻个人财富与竞争对手财富差的效用。首先,我们应用动态规划原理,得出了相应值函数所满足的HJB方程。然后,得到了在幂期望效用框架下非零和博弈的均衡投资策略和值函数的显式表达。最后,借助数值模拟,分析了模型中的参数对均衡投资策略和值函数的影响,从而为资产负债管理提供一定的理论指导。  相似文献   

7.
研究Stein-Stein随机波动率模型下带动态VaR约束的最优投资组合选择问题. 假设投资者的目标是最大化终端财富的期望幂效用,可投资于无风险资产和一种风险资产, 风险资产的价格过程由Stein-Stein随机波动率模型刻画. 同时, 投资者期望能在投资过程中利用动态VaR约束控制所面对的风险.运用Bellman动态规划方法和Lagrange乘子法, 得到了该约束问题最优策略的解析式及特殊情形下最优值函数的解析式; 并通过理论分析和数值算例, 阐述了动态VaR约束与随机波动率对最优投资策略的影响.  相似文献   

8.
研究带泊松跳的线性Markov切换系统的随机微分博弈问题,首先在有限时域内,借助动态规划原理和配方法,得到了Nash均衡解存在的条件等价于其相应的微分Riccati方程存在解,并给出了均衡解及最优性能泛函值函数的显式表达.然后延伸到无限时域进行分析,得到了Nash均衡解存在的条件等价于其相应的代数Riccati方程存在解.最后讨论了金融市场中的投资组合的最优化问题,假设风险资产的价格服从带Markov切换参数的跳扩散过程,两个投资者在相互竞争的情形下进行非零和随机微分投资博弈,利用上述结论得到了最优投资组合策略的解.  相似文献   

9.
本文研究了n个保险公司之间的非零和随机微分投资再保险博弈问题.每个保险公司可以购买比例再保险,并将财富投资于一个由无风险资产,可违约债券和n个风险资产组成的金融市场.特别地,风险资产的价格过程服从CEV模型,可违约债券可在违约时收回一定比例的价值.每个保险公司的目标是相对于竞争对手,最大化终端财富的期望指数效用.利用随机最优控制理论,我们分别推导了均衡策略和均衡值函数的显式表达式.数值例子分析了模型参数对均衡策略的影响.此外,我们还分析了保险公司数量对均衡投资策略的影响.我们发现,随着保险公司数量的增加,每个保险公司将在风险资产和可违约债券上投入更多的资金.  相似文献   

10.
建立了Cox-Ingersoll—Ross随机利率下的关于两个投资者的投资组合效用微分博弈模型.市场利率具有CIR动力,博弈双方存在唯一的损益函数,损益函数取决于投资者的投资组合财富.一方选择动态投资组合策略以最大化损益函数,而另一方则最小化损益函数.运用随机控制理论,在一般的效用函数下得到了基于效用的博弈双方的最优策略.特别考虑了常数相对风险厌恶情形,获得了显示的最优投资组合策略和博弈值.最后给出了数值例子和仿真结果以说明本文的结论.  相似文献   

11.
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.  相似文献   

12.
??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.  相似文献   

13.
This paper investigates the implications of strategic interaction (i.e., competition) between two CARA insurers on their reinsurance-investment policies. The two insurers are concerned about their terminal wealth and the relative performance measured by the difference in their terminal wealth. The problem of finding optimal policies for both insurers is modelled as a non-zero-sum stochastic differential game. The reinsurance premium is calculated using the variance premium principle and the insurers can invest in a risk-free asset, a risky asset with Heston’s stochastic volatility and a defaultable corporate bond. We derive the Nash equilibrium reinsurance policy and investment policy explicitly for the game and prove the corresponding verification theorem. The equilibrium strategy indicates that the best response of each insurer to the competition is to mimic the strategy of its opponent. Consequently, either the reinsurance strategy or the investment strategy of an insurer with the relative performance concern is riskier than that without the concern. Numerical examples are provided to demonstrate the findings of this study.  相似文献   

14.
The aim of this work is to investigate a portfolio optimization problem in presence of fixed transaction costs. We consider an economy with two assets: one risky, modeled by a geometric Brownian motion, and one risk-free which grows at a certain fixed rate. The agent is fully described by his/her utility function and the objective is to maximize the expected utility from the liquidation of wealth at a terminal date. We deal with different forms of utility functions (power, logarithmic and exponential utility), describing in each case how the fixed transaction costs influence the agent’s behavior. We show when it is optimal to recalibrate his/her portfolio and which are the best adjusted portfolios. We also analyze how the optimal strategy is influenced by the risk-aversion, as well as other model parameters.  相似文献   

15.
In this article, we study a multi-period portfolio selection model in which a generic class of probability distributions is assumed for the returns of the risky asset. An investor with a power utility function rebalances a portfolio comprising a risk-free and risky asset at the beginning of each time period in order to maximize expected utility of terminal wealth. Trading the risky asset incurs a cost that is proportional to the value of the transaction. At each time period, the optimal investment strategy involves buying or selling the risky asset to reach the boundaries of a certain no-transaction region. In the limit of small transaction costs, dynamic programming and perturbation analysis are applied to obtain explicit approximations to the optimal boundaries and optimal value function of the portfolio at each stage of a multi-period investment process of any length.  相似文献   

16.
We study optimal asset allocation in a crash-threatened financial market with proportional transaction costs. The market is assumed to be either in a normal state, in which the risky asset follows a geometric Brownian motion, or in a crash state, in which the price of the risky asset can suddenly drop by a certain relative amount. We only assume the maximum number and the maximum relative size of the crashes to be given and do not make any assumptions about their distributions. For every investment strategy, we identify the worst-case scenario in the sense that the expected utility of terminal wealth is minimized. The objective is then to determine the investment strategy which yields the highest expected utility in its worst-case scenario. We solve the problem for utility functions with constant relative risk aversion using a stochastic control approach. We characterize the value function as the unique viscosity solution of a second-order nonlinear partial differential equation. The optimal strategies are characterized by time-dependent free boundaries which we compute numerically. The numerical examples suggest that it is not optimal to invest any wealth in the risky asset close to the investment horizon, while a long position in the risky asset is optimal if the remaining investment period is sufficiently large.  相似文献   

17.
In this paper, we study the stochastic Nash equilibrium portfolio game between two pension funds under inflation risks. The financial market consists of cash, bond and two stocks. It is assumed that the price index is derived through a generalized Fisher equation while the bond is related to the price index to hedge the risk of inflation. Besides, these two pension managers can invest in their familiar stocks. The goal of the pension managers is to maximize the utility of the weighted terminal wealth and relative wealth. Dynamic programming method is employed to derive the Nash equilibrium strategies. In the end, a numerical analysis is presented to reveal the economic behaviors of the two DC pension funds.  相似文献   

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