共查询到20条相似文献,搜索用时 98 毫秒
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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
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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
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利用破产理论和随机控制理论研究保险基金最优投资策略,建立生存概率最大化的目标函数,得到最优投资策略满足的随机微分方程;在初始金逼近0时得到保险基金的最优投资策略的显示解;采用递推算法,得到初始准备金为任意值时的最优投资策略. 相似文献
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在连续时间模型假设下,研究风险资产价格服从一个带有随机波动的几何布朗运动的最优消费和投资问题.首先建立了最优消费和投资同题随机最优控制数学模型;然后运用随机最优控制理论,得到了最优投资和消费随机最优控制问题的值函数所满足的线性抛物线偏微分方程和非线性抛物线偏微分方程. 相似文献
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Stochastic optimal control of DC pension funds 总被引:1,自引:0,他引:1
In this paper, we study the portfolio problem of a pension fund manager who wants to maximize the expected utility of the terminal wealth in a complete financial market with the stochastic interest rate. Using the method of stochastic optimal control, we derive a non-linear second-order partial differential equation for the value function. As it is difficult to find a closed form solution, we transform the primary problem into a dual one by applying a Legendre transform and dual theory, and try to find an explicit solution for the optimal investment strategy under the logarithm utility function. Finally, a numerical simulation is presented to characterize the dynamic behavior of the optimal portfolio strategy. 相似文献
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Mohamed Mnif 《Applied Mathematics and Optimization》2007,56(2):243-264
In this paper we are interested in an investment problem with stochastic volatilities and portfolio constraints on amounts.
We model the risky assets by jump diffusion processes and we consider an exponential utility function. The objective is to
maximize the expected utility from the investor terminal wealth. The value function is known to be a viscosity solution of
an integro-differential Hamilton-Jacobi-Bellman (HJB in short) equation which could not be solved when the risky assets number
exceeds three. Thanks to an exponential transformation, we reduce the nonlinearity of the HJB equation to a semilinear equation.
We prove the existence of a smooth solution to the latter equation and we state a verification theorem which relates this
solution to the value function. We present an example that shows the importance of this reduction for numerical study of the
optimal portfolio. We then compute the optimal strategy of investment by solving the associated optimization problem. 相似文献
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In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis. 相似文献
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本文提出了一种新的带有时间幂次项的灰色GM(1,1,k,k2)模型,给出了其灰微分方程和白化微分方程基本形式。基于最小二乘法获得了该模型参数估计值,并推导了该模型时间响应函数。鉴于GM(1,1,k,k2)模型灰微分方程与白化微分方程之间存在跳跃关系,首先对灰微分方程的背景值进行了优化,并推导了优化后的背景值计算公式。为了克服初始值的影响,根据误差平方和最小,进一步优化了GM(1,1,k,k2)模型时间响应函数。最后,该优化后的GM(1,1,k,k2)模型被应用于软土地基沉降预测,获得了较好的模拟预测效果,说明模型是可行的。 相似文献
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I. V. Volovich V. Zh. Sakbaev 《Proceedings of the Steklov Institute of Mathematics》2014,285(1):56-80
A new statement of a boundary value problem for partial differential equations is discussed. An arbitrary solution to a linear elliptic, hyperbolic, or parabolic second-order differential equation is considered in a given domain of Euclidean space without any constraints imposed on the boundary values of the solution or its derivatives. The following question is studied: What conditions should hold for the boundary values of a function and its normal derivative if this function is a solution to the linear differential equation under consideration? A linear integral equation is defined for the boundary values of a solution and its normal derivative; this equation is called a universal boundary value equation. A universal boundary value problem is a linear differential equation together with a universal boundary value equation. In this paper, the universal boundary value problem is studied for equations of mathematical physics such as the Laplace equation, wave equation, and heat equation. Applications of the analysis of the universal boundary value problem to problems of cosmology and quantum mechanics are pointed out. 相似文献
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A. I. Subbotin 《Journal of Optimization Theory and Applications》1984,43(1):103-133
We consider feedback, two-person, zero-sum differential games. We obtain two inequalities for the directional derivatives of the nonsmooth value function. We show that these inequalities, together with the boundary conditions, constitute necessary and sufficient conditions which the value function must satisfy. In the region where the value function is differentiable, the inequalities become the well-known main equation of differential game theory (Isaacs-Bellman equation). The results obtained here may be useful in the approximation of the value function by piecewise smooth splines and also in the classification of singular surfaces.The author would like to thank Academician N. N. Krasovskii for his valuable advice and encouragement. 相似文献
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This paper investigates the optimal reinsurance and investment in a hidden Markov financial market consisting of non-risky (bond) and risky (stock) asset. We assume that only the price of the risky asset can be observed from the financial market. Suppose that the insurance company can adopt proportional reinsurance and investment in the hidden Markov financial market to reduce risk or increase profit. Our objective is to maximize the expected exponential utility of the terminal wealth of the surplus of the insurance company. By using the filtering theory, we establish the separation principle and reduce the problem to the complete information case. With the help of Girsanov change of measure and the dynamic programming approach, we characterize the value function as the unique solution of a linear parabolic partial differential equation and obtain the Feynman-Kac representation of the value function. 相似文献
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This paper studies the optimal consumption–investment–reinsurance problem for an insurer with a general discount function and exponential utility function in a non-Markovian model. The appreciation rate and volatility of the stock, the premium rate and volatility of the risk process of the insurer are assumed to be adapted stochastic processes, while the interest rate is assumed to be deterministic. The object is to maximize the utility of intertemporal consumption and terminal wealth. By the method of multi-person differential game, we show that the time-consistent equilibrium strategy and the corresponding equilibrium value function can be characterized by the unique solutions of a BSDE and an integral equation. Under appropriate conditions, we show that this integral equation admits a unique solution. Furthermore, we compare the time-consistent equilibrium strategies with the optimal strategy for exponential discount function, and with the strategies for naive insurers in two special cases. 相似文献