共查询到20条相似文献,搜索用时 62 毫秒
1.
本文在半鞅理论框架下,构建包括可交易风险资产、不可交易风险资产和未定权益的金融投资模型。在考虑随机通胀风险和获取部分市场信息的情形下,研究投资经理人终端真实净财富指数效用最大化问题。运用滤波理论、半鞅和倒向随机微分方程(BSDE)理论,求解带有随机通胀风险的最优投资策略和价值过程精确解。数值分析结果发现,可交易风险资产最优投资额随着预期通胀率的增加而减少,投资价值呈先增后减态势。当通胀波动率无限接近可交易风险资产名义价格波动率时,通胀风险可完全对冲,投资人会不断追加在可交易风险资产的投资额,以期实现终端真实净财富期望指数效用最大化。研究结果为金融市场的投资决策提供更加科学的理论参考。 相似文献
2.
本文研究具有随机保费和交易费用的最优投资和再保险策略选择问题.保险公司的盈余通过跳-扩散过程来模拟,假设保费收入是随机的.我们的研究目标是寻找一个最优再保险和投资策略,最大化投资终止时刻财富的期望效用.应用随机控制理论,我们得到最优投资-再保险策略和值函数的显式解.通过数值计算,我们给出模型参数对最优策略的影响.结果揭示了一些令人感兴趣的现象,它们可以对实际中的再保险和投资予以指导. 相似文献
3.
本文讨论有风险控制的最优控制组合问题并研究了倍率风险函数及临界风险的性质,最大最小风险的估计,给出了其倍率-风险函数有严格解析形式的例子。 相似文献
4.
现代金融经济中的很多问题可以构建成随机控制模型,而随机控制的求解却存在一定的困难.马氏链算法应该是一种有效的求解随机控制问题的数值方法.本文以Claus Munk的工作为基础,针对一类最优投资模型,具体确定了马氏链的转移矩阵并证明其满足算法收敛条件,并用MATLAB语言编成一个程序实现. 相似文献
5.
对跳-扩散风险模型,研究了最优投资和再保险问题.保险公司可以购买再保险减少理赔,保险公司还可以把盈余投资在一个无风险资产和一个风险资产上.假设再保险的方式为联合比例-超额损失再保险.还假设无风险资产和风险资产的利率是随机的,风险资产的方差也是随机的.通过解决相应的Hamilton-Jacobi-Bellman(HJB)方程,获得了最优值函数和最优投资、再保险策略的显示解.特别的,通过一个例子具体的解释了得到的结论. 相似文献
6.
在经典复合泊松模型中,保险公司将资金投入一个风险投资过程和一个无风险投资过程.当索赔的分布确定后,运用随机控制中的HJB方程最小化保险公司的破产概率,在已知投资规模或投资组合的情况下求解二者中的另一项,进而得到最优投资策略并讨论各种策略的运用对破产概率的影响.解决保险公司的投资资金分配问题,在实际应用中具有一定的参考价值. 相似文献
7.
本文讨论了具有交易成本与时变波动的最优投资问题。在此模型中,当风险溢价与方差成线性关系时,最优策略与波动水平无关。 相似文献
8.
9.
10.
11.
投资组合和具有跳跃-扩散过程再保险的最优控制 总被引:1,自引:0,他引:1
该文考虑了投资和具有跳跃-扩散过程的受限的超额损失再保险模型,针对再保险保费是期望值原理,目标函数为指数效用的情况,得到了投资、免赔额和限制额的最优控制及相应的值函数的表达式. 相似文献
12.
13.
This paper treats a finite time horizon optimal control problem in which the controlled state dynamics are governed by a general system of stochastic functional differential equations with a bounded memory. An infinite dimensional Hamilton–Jacobi–Bellman (HJB) equation is derived using a Bellman-type dynamic programming principle. It is shown that the value function is the unique viscosity solution of the HJB equation. 相似文献
14.
Federica Masiero 《随机分析与应用》2013,31(4):877-902
Abstract We consider stochastic optimal control problems in Banach spaces, related to nonlinear controlled equations with dissipative non linearities: on the nonlinear term we do not impose any growth condition. The problems are treated via the backward stochastic differential equations approach, that allows also to solve in mild sense Hamilton Jacobi Bellman equations in Banach spaces. We apply the results to controlled stochastic heat equation, in space dimension 1, with control and noise acting on a subdomain. 相似文献
15.
Optimal Proportional Reinsurance for Controlled Risk Process which is Perturbed by Diffusion 总被引:4,自引:0,他引:4
Zhi-bin Liang 《应用数学学报(英文版)》2007,23(3):477-488
In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases. 相似文献
16.
A continuous time stochastic model is used to study a hybrid pension plan, where both the contribution and benefit levels are adjusted depending on the performance of the plan, with risk sharing between different generations. The pension fund is invested in a risk-free asset and multiple risky assets. The objective is to seek an optimal investment strategy and optimal risk-sharing arrangements for plan trustees and participants so that this proposed hybrid pension system provides adequate and stable income to retirees while adjusting contributions effectively, as well as keeping its sustainability in the long run. These goals are achieved by minimizing the expected discount disutility of intermediate adjustment for both benefits and contributions and that of terminal wealth in finite time horizon. Using the stochastic optimal control approach, closed-form solutions are derived under quadratic loss function and exponential loss function. Numerical analysis is presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market and how the optimal benefit changes with respect to different risk aversions. Through numerical analysis, we find that the optimal strategies do adjust the contributions and retirement benefits according to fund performance and model objectives so the intergenerational risk sharing seem effectively achieved for this collective hybrid pension plan. 相似文献
17.
本文对索赔次数为复合Poisson-Geometric过程的风险模型,在保险公司的盈余可以投资于风险资产,以及索赔购买比例再保险的策略下,研究使得破产概率最小的最优投资和再保险策略.通过求解相应的Hamilton-Jacobi-Bellman方程,得到使得破产概率最小的最优投资和比例再保险策略,以及最小破产概率的显示表达式. 相似文献
18.
Qingxin Meng 《随机分析与应用》2013,31(1):88-109
In this article, we consider a linear-quadratic optimal control problem (LQ problem) for a controlled linear stochastic differential equation driven by a multidimensional Browinan motion and a Poisson random martingale measure in the general case, where the coefficients are allowed to be predictable processes or random matrices. By the duality technique, the dual characterization of the optimal control is derived by the optimality system (so-called stochastic Hamilton system), which turns out to be a linear fully coupled forward-backward stochastic differential equation with jumps. Using a decoupling technique, the connection between the stochastic Hamilton system and the associated Riccati equation is established. As a result, the state feedback representation is obtained for the optimal control. As the coefficients for the LQ problem are random, here, the associated Riccati equation is a highly nonlinear backward stochastic differential equation (BSDE) with jumps, where the generator depends on the unknown variables K, L, and H in a quadratic way (see (5.9) herein). For the case where the generator is bounded and is linearly dependent on the unknown martingale terms L and H, the existence and uniqueness of the solution for the associated Riccati equation are established by Bellman's principle of quasi-linearization. 相似文献
19.
In this paper, the insurer is allowed to buy reinsurance and allocate his money among three financial securities: a defaultable corporate zero-coupon bond, a default-free bank account, and a stock, while the instantaneous rate of the stock is described by an Ornstein-Uhlenbeck process. The objective is to maximize the exponential utility of the terminal wealth. We decompose the original optimization problem into two subproblems: a pre-default case and a post-default case.
Using dynamic programming principle, and then solving the corresponding HJB equations, we derive the closed-form solutions for the optimal reinsurance and investment strategies and the corresponding value functions 相似文献
20.
FeiWeiyin WuRangquan 《高校应用数学学报(英文版)》2000,15(3):350-358
This paper considers a consumption and investment decision problem with a higher interest rate for borrowing as well as the dividend rate. Wealth is divided into a riskless asset and risky asset with logrithmic Erownian motion price fluctuations. The stochastic control problem of maximizating expected utility from terminal wealth and consumption is studied. Equivalent conditions for optimality are obtained. By using duality methods ,the existence of optimal portfolio consumption is proved,and the explicit solutions leading to feedback formulae are derived for deteministic coefficients. 相似文献