再保险-投资的M-V及M-VaR最优策略

考虑保险公司再保险-投资问题在均值-方差(M-V)模型和均值-在险价值(M-VaR)模型下的最优常数再调整策略.在保险公司盈余过程服从扩散过程的假设及多风险资产的Black-Scholes市场条件下,分别得到均值-方差模型和均值-在险价值模型下保险公司再保险-投资问题的最优常数再调整策略及共有效前沿,并就两种模型下的结...     

奈特不确定下资产收益率发生紊乱的最优投资策略

在部分信息且市场利率非零的情形下,应用α-极大极小期望效用(α-MEU)模型区别投资者的含糊和含糊态度,研究资产预期收益率发生紊乱(disorder)时的投资组合问题.首先,利用倒向随机微分方程理论刻画了α-MEU.其次,给出紊乱时刻的后验概率过程满足的随机微分方程(SDE),以及价值过程所满足的倒向随机微分方程(BSDE).最后,应用鞅论解出指数效用时的最优交易策略和价值过程的明确表达式.     

基于新巴塞尔协议监管下保险人的均值-方差最优投资-再保险问题

本文研究了均值-方差优化准则下,保险人的最优投资和最优再保险问题.我们用一个复合泊松过程模型来拟合保险人的风险过程,保险人可以投资无风险资产和价格服从跳跃-扩散过程的风险资产.此外保险人还可以购买新的业务(如再保险).本文的限制条件为投资和再保险策略均非负,即不允许卖空风险资产,且再保险的比例系数非负.除此之外,本文还引入了新巴塞尔协议对风险资产进行监管,使用随机二次线性(linear-quadratic,LQ)控制理论推导出最优值和最优策略.对应的哈密顿-雅克比-贝尔曼(Hamilton-Jacobi-Bellman,HJB)方程不再有古典解.在粘性解的框架下,我们给出了新的验证定理,并得到有效策略(最优投资策略和最优再保险策略)的显式解和有效前沿.     

具有一般跳过程的期权无差异效用价值过程的定价模型

本文采用指数效用最大化的方法研究了期权的动态无差异效用价值过程Ct(H;α).考虑股票价格过程为具有基于随机测度的一般跳的半鞅模型,且期权的无差异效用价值过程的Doob-Meyer分解的鞅部分的GKW(Galtchouk-Kunita-Watanabe)分解满足Jacod鞅表示定理.利用无差异效用价值过程在最小熵测度和最优投资策略下为鞅的事实构建了一个倒向随机微分方程.通过概率测度变换将方程的鞅部分和生成元转化为BMO(bounded mean oscillation)鞅,证明了该方程的解的唯一性.并将方程的生成元分成[?A=0]和[?A≠0],证明了最优投资策略存在.从而给出期权无差异效用价值过程的倒向随机微分方程的表达形式.     

带有离散个体等级结构的种群系统的控制问题

提出一类基于离散个体等级结构的非线性种群模型,研究它的相关控制问题,包括系统可控性、镇定与最优收获问题.证明了系统的上(下)可控性、精确可控性和镇定性.仔细刻画了最优收获策略,对三类情形给出了具体的收获强度公式.通过数值模拟分析了个体经济价值对最优策略的影响.     

奈特不确定下带通胀的跨国直接投资问题

本文研究了一家公司在含糊下带通胀的跨国直接投资(FDI)问题.利用Ito公式推导出含糊下考虑通胀因素的消费篮子价格动力学方程.结合公司进行跨国投资决策时需要缴纳的法人税,给定了跨国直接投资的价值,并在通胀折现的跨国直接投资价值最大化标准下,分析了公司进行(不可逆)跨国直接投资的最优时间,通过解HJB方程推导出了公司由出口转向跨国直接投资时的最优GDP水平.通过进行数值模拟,定量分析了通胀因素对公司跨国直接投资策略的影响.     

考虑破产惩罚的对偶风险模型的最优控制

本文主要研究对偶风险模型的最优控制问题. 为了考虑破产对保险公司(金融机构)的影响, 我们在构造价值函数的过程中引入了一个变量来测度破产对公司盈利的影响. 为了求得最优的控制策略, 我们首先研究了两类带有约束的优化问题. 基于这些带约束优化问题的解, 我们给出了无约束的最优策略.     

道德风险影响下的保险最优投资研究

在考虑道德风险的情况下,以均值方差准则为目标研究保险人最优投资问题.假设保险盈余过程服从C-L模型,金融市场上存在一种无风险资产和一种风险资产可供投资,其中风险资产的价格过程服从几何布朗运动.在纯道德风险保险契约设计中,借鉴相关研究对努力水平和效用化努力成本的假设,量化道德风险对盈余过程的影响.在均值方差目标下,建立保险人最优投资问题的广义Hamilton-Jacobi-Bellman(HJB)方程,给出保险人时间一致的均衡投资策略和价值函数.结果显示累计索赔比例参数越大,公司对最优努力水平越敏感,采取措施降低道德风险有利于公司收益提升;努力成本参数越大,公司会降低努力水平减少支出,避免损失.     

保险公司的最优投资和再保险策略

在保险公司既可以做证券(股票和债券)投资,同时又采取比例再保险策略的情况下,通过对经典的Cramér-Lundberg保险公司盈余过程模型的连续扩散近似,利用动态规划原理分别得出了在破产概率最小和终值期望效用最大两种目标函数下,保险公司的最优投资和最优再保策略的显式解和对应的目标函数值.对两种目标函数下的最优策略做了比较研究.     

Polish空间上的折扣马氏过程量子化策略的渐近优化北大核心CSCD

该文研究了Polish空间上、带折扣因子的连续时间马尔可夫决策过程(CTMDPs)的量子化平稳策略的渐近最优性问题.首先,建立了折扣最优方程(DOE)及其解的存在性和唯一性.其次,在适当的条件下证明了最优确定性平稳策略的存在性.此外,为了对行动空间进行离散化,构造了一列量子化策略,利用有限行动空间的策略来逼近一般(Polish)空间上的折扣CTMDPs最优平稳策略.最后,通过一个例子来说明该文的渐近逼近结果.     

关于运输问题最优解的进一步讨论

首先给出了运输问题最优解的相关概念,将最优解扩展到广义范畴,提出狭义多重最优解和广义多重最优解的概念及其区别.然后给出了惟一最优解、多重最优解、广义有限多重最优解、广义无限多重最优解的判定定理及其证明过程.最后推导出了狭义有限多重最优解个数下限和广义有限多重最优解个数上限的计算公式,并举例验证了结论的正确性.     

A numerical method for an optimal control problem with minimum sensitivity on coefficient variation

In this paper, we consider a class of optimal control problem involving an impulsive systems in which some of its coefficients are subject to variation. We formulate this optimal control problem as a two-stage optimal control problem. We first formulate the optimal impulsive control problem with all its coefficients assigned to their nominal values. This becomes a standard optimal impulsive control problem and it can be solved by many existing optimal control computational techniques, such as the control parameterizations technique used in conjunction with the time scaling transform. The optimal control software package, MISER 3.3, is applicable. Then, we formulate the second optimal impulsive control problem, where the sensitivity of the variation of coefficients is minimized subject to an additional constraint indicating the allowable reduction in the optimal cost. The gradient formulae of the cost functional for the second optimal control problem are obtained. On this basis, a gradient-based computational method is established, and the optimal control software, MISER 3.3, can be applied. For illustration, two numerical examples are solved by using the proposed method.     

基于腐损程度的季节性产品动态定价与订单量的集成优化

为了对易腐季节性产品的销售价格和订单量进行最优决策,考虑产品在不同腐损程度的情形下,需求与价格和时间同时相关的一类季节性产品的动态定价和订单量的集成优化问题.建立该类产品的价格制订次数、每次制订的价格和订单量的集成优化模型,并对模型进行求解,最后结合数例验证模型的实用性和可操作性,并分析产品腐损程度对价格制订次数、价格大小、订单量和利润的影响.结果表明,随着产品腐损程度的提高,零售商在销售季节内的产品价格最优制订次数保持不变;零售商在销售季节内所制订的最优价格逐渐微降;产品的最优订单量和所产生的最优利润逐渐微升.     

Transient and steady-state analysis of a manufacturing system with setup changes

This paper deals with the optimal scheduling of a one-machine two-product manufacturing system with setup, operating in a continuous time dynamic environment. The machine is reliable. A known constant setup time is incurred when switching over from a part to the other. Each part has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a production flow control problem. The objective is to minimize the sum of the backlog and inventory costs incurred over a finite planning horizon. The global optimal solution, expressed as an optimal feedback control law, provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady-state, the optimal cyclic schedule (Limit Cycle) is determined. This is equivalent to solving a one-machine two-product Lot Scheduling Problem. To solve the transient case, the system's state space is partitioned into mutually exclusive regions such that with each region is associated an optimal control policy. A novel algorithm (Direction Sweeping Algorithm) is developed to obtain the optimal state trajectory (optimal policy that minimizes the sum of inventory and backlog costs) for this last case.     

Nonlinear optimal feedback control for lunar module soft landing

In this paper, the task of achieving the soft landing of a lunar module such that the fuel consumption and the flight time are minimized is formulated as an optimal control problem. The motion of the lunar module is described in a three dimensional coordinate system. We obtain the form of the optimal closed loop control law, where a feedback gain matrix is involved. It is then shown that this feedback gain matrix satisfies a Riccati-like matrix differential equation. The optimal control problem is first solved as an open loop optimal control problem by using a time scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, we present a practical method to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results show that the proposed approach is highly effective.     

Solvency II,regulatory capital,and optimal reinsurance: How good are Conditional Value-at-Risk and spectral risk measures?

We study the problem of optimal reinsurance as a means of risk management in the regulatory framework of Solvency II under Conditional Value-at-Risk and, as its natural extension, spectral risk measures. First, we show that stop-loss reinsurance is optimal under both Conditional Value-at-Risk and spectral risk measures. Spectral risk measures thus constitute a more general class of suitable regulatory risk measures than specific Conditional Value-at-Risk. At the same time, the established type of stop-loss reinsurance can be maintained as the optimal risk management strategy that minimizes regulatory capital. Second, we derive the optimal deductibles for stop-loss reinsurance. We show that under Conditional Value-at-Risk, the optimal deductible tends towards restrictive and counter-intuitive corner solutions or “plunging”, which is a serious objection against its use in regulatory risk management. By means of the broader class of spectral risk measures, we are able to overcome this shortcoming as optimal deductibles are now interior solutions. Especially, the recently discussed power spectral risk measures and the Wang risk measure are shown to avoid any plunging. They yield a one-to-one correspondence between the risk parameter and the optimal deductible and, thus, provide economically plausible risk management strategies.     

一类具有年龄结构的非线性种群扩散系统的最优收获控制

讨论了一类与年龄相关的非线性种群扩散系统的最优收获控制问题,证明了最优收获控制的存在性,并且给出了控制为最优的必要条件及其由偏微分方程组和变分不等式组成的最优性组.这些结果可为种群扩散系统最优控制问题的实际研究提供理论基础.     

A computational method for free terminal time optimal control problem governed by nonlinear time delayed systems

This paper considers a free terminal time optimal control problem governed by nonlinear time delayed system, where both the terminal time and the control are required to be determined such that a cost function is minimized subject to continuous inequality state constraints. To solve this free terminal time optimal control problem, the control parameterization technique is applied to approximate the control function as a piecewise constant control function, where both the heights and the switching times are regarded as decision variables. In this way, the free terminal time optimal control problem is approximated as a sequence of optimal parameter selection problems governed by nonlinear time delayed systems, each of which can be viewed as a nonlinear optimization problem. Then, a fully informed particle swarm optimization method is adopted to solve the approximate problem. Finally, two free terminal time optimal control problems, including an optimal fishery control problem, are solved by using the proposed method so as to demonstrate its applicability.     

Optimal payout policy in presence of downside risk

We analyze the determination of a value maximizing dividend payout policy for a broad class of cash reserve processes modeled as spectrally negative jump diffusions. We extend previous results based on continuous diffusion models and characterize the value of the optimal dividend distribution strategy explicitly. We also characterize explicitly the values as well as the optimal dividend thresholds for a class of associated optimal liquidation and sequential lump sum dividend control problems. Our results indicate that both the value as well as the marginal value of the optimal policies are increasing functions of policy flexibility in the discontinuous setting as well.      

Limiting behavior of bang-bang controls for Sobolev problems

We consider the limiting behavior of optimal bang-bang controls as a family of Sobolev equations formally converges to a wave equation. The weak-starlimit of the sequence of bang-bang controls is an optimal control for the wave equation problem. The associated optimal states converge strongly and, for the optimal time problem, the optimal times converge to the optimal time for the wave equation.This work was supported in part by the National Science Foundation, Grant No. MCS-79-02037.