最优再保险及投资组合策略问题

为规避风险的巨大波动,保险公司会将承保的理赔进行分保,即再保险.假定再保险公司采用方差保费准则从保险公司收取保费.应用扩散逼近模型,刻画了保险公司有再保险控制下的资本盈余.另外,保险公司的盈余允许投资到利率、股票等金融市场.通过控制再保险及投资组合策略,研究了最小破产概率.应用动态规划方法(Hamilton-Jacobi-Bellman方程),对最小破产概率、最优再保险及投资组合策略给出了明晰解答,并给出了数值直观分析.     

经典风险模型下CEV股票市场中最优再保险和投资策略（英文）

本文在复合泊松跳索赔模型下,考虑保险公司投资于常弹性方差(CEV)金融市场和购买比例-超额损失组合再保险的最优策略.在期望效用最大化准则下,利用随机控制技巧,证明了,事实上,保险公司的最优再保险策略等同于要么购买一个纯超额损失再保险,要么购买一个纯比例再保险.进一步给出两种情形下的最优再保险和投资策略以及值函数的表达式.     

CEV模型下最大化HARA效用的最优再保险与投资策略

在风险资产价格服从CEV模型时,考虑保险公司为最大化双曲绝对风险厌恶(HARA)效用的最优投资与再保险问题.假定保险公司的索赔过程为带漂移的布朗运动,且保险公司通过购买比例再保险来转移索赔风险,运用随机控制理论和Legendre变换方法得到了最优策略的显示表达式.     

基于股票价格随机脉冲模型的保险人再保险和投资的最优动态组合选择

本文假设保险人可以进行再保险,并且允许其在金融市场中将资产投资于风险资产和无风险资产,其中风险资产价格采用随机脉冲模型来刻画.当目标是最大化在某一确定终止时刻所拥有财富的二次效用函数期望时,分别得到了超额损失再保险和比例再保险情况下保险人的再保险和投资最优动态选择的显式解和闭解.利用得到的显式解,考虑了金融风险和保险风险之间相关性对最优动态选择的影响,做了相关数值计算.     

固定支付下养老基金资产组合CEV模型及最优投资策略

在固定支付水平的条件之下,就养老基金资产组合问题建立常方差弹性(CEV)模型,应用随机控制原理求出了相应的非线性Hamilton-Jacobi-Bellman偏微方程,再用Legendre变换将其转化为线性偏微方程,建立对偶问题.通过对偶问题的求解,从而求得原问题的精确解析解,确定风险资产和无风险资产的最优投资比例,实现了满足养老基金既定支出水平下总资产的对数效用最大化,从实际市场的角度改进发展了经典的Merton模型结果.     

带交易费用的最优投资和比例再保险

研究了保险公司的最优投资和再保险问题.保险公司的盈余通过跳-扩散风险模型来模拟,可以把盈余的一部分投资到金融市场,金融市场由一个无风险资产和n个风险资产组成,并且保险公司还可以购买比例再保险;在买卖风险资产时,考虑了交易费用.通过随机控制的理论,获得了最优策略和值函数的显示解.     

投资影响下的再保险策略

本文研究了投资影响下的再保险策略,利用有关的线性正倒向随机微分方程,获得投资影响下再保险的自留比例或自留额的计算式子.     

养老基金投资组合的常方差弹性(CEV)模型和解析决策

针对以年金形式发放待遇的缴费预定制养老基金,在退休前和退休后的两个阶段,分别构建了常方差弹性(CEV)模型,并应用Legendre变换将原问题转化为对偶问题,在追求指数效用最大化的条件下,求得了精确解析解,从而确定了这两个阶段的最优投资决策．     

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.     

Vasicek利率与Heston模型下的最优投资和再保险

本文主要研究Vasicek随机利率模型下保险公司的最优投资与再保险问题.假设保险公司的盈余过程由带漂移的布朗运动来描述,保险公司通过购买比例再保险来转移索赔风险;同时,将财富投资于由一种无风险资产与一种风险资产组成的金融市场,其中,利率期限结构服从Vasicek利率模型,且风险资产价格过程满足Heston随机波动率模型.利用动态规划原理及变量替换的方法,得到了指数效用下最优投资与再保险策略的显示表达式,并给出数值例子分析了主要模型参数对最优策略的影响.     

Pinning consensus control for switched multi-agent systems: A switched adaptive dynamic programming method

Stability is fundamental to ensure the operation of control system, but optimality is the ultimate goal to achieve the maximum performance. This paper investigates an event-triggered pinning optimal consensus control for switched multi-agent system (SMAS) via a switched adaptive dynamic programming (ADP) method. The technical contribution mainly lies in two aspects. On the one hand, in order to optimize the control performance and ensure the consensus, the switched local value function (SLVF) and the minimum-error switching law are constructed. Based on SLVF, an algorithm of switched ADP policy iteration is proposed, and its convergence and optimality are proved. On the other hand, considering that it is impractical to install a controller for each agent in reality, a pinning strategy is developed to guide the setting of the ADP controller, which can reduce the waste of control resources. A new condition is constructed to determine the minimum number of controlled vertices of the SMAS. Lastly, a numerical example is given to verify the effectiveness of the proposed method.     

Efficient dynamic programming implementations of Newton's method for unconstrained optimal control problems

Naive implementations of Newton's method for unconstrainedN-stage discrete-time optimal control problems with Bolza objective functions tend to increase in cost likeN ³ asN increases. However, if the inherent recursive structure of the Bolza problem is properly exploited, the cost of computing a Newton step will increase only linearly withN. The efficient Newton implementation scheme proposed here is similar to Mayne's DDP (differential dynamic programming) method but produces the Newton step exactly, even when the dynamical equations are nonlinear. The proposed scheme is also related to a Riccati treatment of the linear, two-point boundary-value problems that characterize optimal solutions. For discrete-time problems, the dynamic programming approach and the Riccati substitution differ in an interesting way; however, these differences essentially vanish in the continuous-time limit.This work was supported by the National Science Foundation, Grant No. DMS-85-03746.     

Adaptive neural dynamic surface control with fixed-time prescribed performance for uncertain nonstrict-feedback stochastic switched systems

An adaptive neural dynamic surface control (DSC) problem with fixed-time prescribed performance (FTPP) is investigated for a class of nonstrict-feedback stochastic switched systems. Differently from the existing works for FTPP problem, the stochastic switched systems with nonstrict-feedback form and completely unknown systems are considered in this paper, and the unknown functions are approximated by some radial basis function (RBF) neural networks (NNs). The desired adaptive neural controller is designed by using common Lyapunov function method and defining fixed-time prescribed performance function (PPF). And based on the adaptive DSC scheme with the nonlinear filter, the “explosion of complexity” problem is avoided. Besides, the constructed fixed-time PPF just need to meet the requirement of second derivative exists. According to the Lyapunov stability theory, the FTPP of output tracking error is achieved, and all signals of closed-loop system remain bounded in probability. Finally, simulation results are presented to verify the availability of the designed control strategy.     

A new method of proving structural properties for certain class of stochastic dynamic control problems

This paper introduces the multimodularity concept to study structural properties for certain class of stochastic dynamic control problems through a new efficient approach. We demonstrate that this approach can substantially simplify the proofs of the main results of one recent article and provide an alternative method for two other models in the literature.     

Identifier-based adaptive neural dynamic surface control for uncertain DC-DC buck converter system with input constraint

In this paper, an identifier-based adaptive neural dynamic surface control (IANDSC) is proposed for the uncertain DC-DC buck converter system with input constraint. Based on the analysis of the effect of input constraint in the buck converter, the neural network compensator is employed to ensure the controller output within the permissible range. Subsequently, the constrained adaptive control scheme combined with the neural network compensator is developed for the buck converter with uncertain load current. In this scheme, a newly presented finite-time identifier is utilized to accelerate the parameter tuning process and to heighten the accuracy of parameter estimation. By utilizing the adaptive dynamic surface control (ADSC) technique, the problem of “explosion of complexity” inherently in the traditional adaptive backstepping design can be overcome. The proposed control law can guarantee the uniformly ultimate boundedness of all signals in the closed-loop system via Lyapunov synthesis. Numerical simulations are provided to illustrate the effectiveness of the proposed control method.     

Differential dynamic programming and Newton's method for discrete optimal control problems

The purpose of this paper is to draw a detailed comparison between Newton's method, as applied to discrete-time, unconstrained optimal control problems, and the second-order method known as differential dynamic programming (DDP). The main outcomes of the comparison are: (i) DDP does not coincide with Newton's method, but (ii) the methods are close enough that they have the same convergence rate, namely, quadratic.The comparison also reveals some other facts of theoretical and computational interest. For example, the methods differ only in that Newton's method operates on a linear approximation of the state at a certain point at which DDP operates on the exact value. This would suggest that DDP ought to be more accurate, an anticipation borne out in our computational example. Also, the positive definiteness of the Hessian of the objective function is easy to check within the framework of DDP. This enables one to propose a modification of DDP, so that a descent direction is produced at each iteration, regardless of the Hessian.Efforts of the first author were partially supported by the South African Council for Scientific and Industrial Research, and those of the second author by NSF Grants Nos. CME-79-05010 and CEE-81-10778.     

Asymptotic method for solving the time-optimal control problem for a nonlinear singularly perturbed system

The time-optimal control problem for a nonlinear singularly perturbed system with multidimensional controls bounded in the Euclidean norm is considered. An algorithm for constructing asymptotic approximations to its solution is proposed. The main advantage of the algorithm is that the original optimal control problem decomposes into two unperturbed problems of lower dimensions.     

Comparison of the cuscore, GLRT and cusum control charts for detecting a dynamic mean change

Although statistical process control (SPC) techniques have been focused mostly on detecting constant mean shifts, dynamic and time-varying process changes frequently occur in the monitoring of feedback-controlled and autocorrelated processes. In this research, the performances of cumulative score (Cuscore), generalized likelihood ratio test (GLRT), and cumulative sum (CUSUM) charts in detecting a dynamic mean change that finally approaches a steady-state value are compared. Theoretical results in average run length (ARL) comparison are provided. From the theretical study we find that, when the steady-state value is greater or less than a critical value,Rδ/2+δ/2, the Cuscore and CUSUM charts have a different performance in detecting the mean change. We prove also that the GLRT has the best performance among the three charts in detecting any mean change for which the steady-state value is not equal to δ or δR, when the in-control ARL is large.     

Structural results for the control of queueing systems using event-based dynamic programming

In this paper we study monotonicity results for optimal policies of various queueing and resource sharing models. The standard approach is to propagate, for each specific model, certain properties of the dynamic programming value function. We propose a unified treatment of these models by concentrating on the events and the form of the value function instead of on the value function itself. This is illustrated with the systematic treatment of one and two-dimensional models. This revised version was published online in June 2006 with corrections to the Cover Date.