考虑状态转换的最优战略调整决策与企业价值研究

宏观经济的变化影响企业战略实施效果,本文构建以状态转换强度为影响因素的企业战略调整优化决策模型.运用随机动态最优控制方法,得到两状态下企业价值解析解,企业当前价值、增长期权和托宾Q分析解,以及相应的最优投资策略.理论研究和数值模拟表明:战略状态不影响企业最优战略调整时机,但影响最优投资支出,高战略水平时,企业生产率更高,为达到并维持企业最优资本结构,企业的投资支出增多;状态转换强度影响企业最优战略调整时机、战略调整瞬时的投资支出、托宾Q值和增长期权-企业价值比值;特别地,相对战略水平阈值是转换概率的单调递增函数,转换概率越大,相对战略水平阈值越大,企业保持当前战略的时间越长.总之,考虑状态转换能够改善未考虑状态转换时制定的战略调整决策和相应投资策略.     

保险公司在二项风险模型下破产概率的渐进估计

主要研究完全离散二项风险模型．在条件系数存在的情况下，得到在破产发生的情况下罚金期望所满足的瑕疵离散更新方程度其渐进解，由此得到了保险公司当初始资本为0时破产概率的显示解和当初始资本μ→∞时的渐进解和破产时刺所发生的赤字分布当初始资本为0时的显示解和当初始资本μ→∞时的渐进解，并在当陪付服从几何分布和赌徒分布的情形下得到了上述特征量的具体结果。     

基于内部竞争的金融企业的最优风险管理

讨论了金融企业的最优管理问题,金融企业的目标是：用于(股东)分红的净收益的期望现值最大,根据Bellman最优性原理,得出了分红情况下的Bellman方程,通过对所得方程的分析给出了解析解和最优控制策略．文章首次提出了最大容忍损失和临界破产概率两个概念,据此给出了破产概率新的解法并得到了企业的临界破产概率和破产原因．     

Optimal Investment with Multiple Risky Assets for an Insurer with Modified Periodic Risk Process

This paper considers the optimal investment problem for an insurer in the sense of maximizing the adjustment coefficient of the risk process.The authors propose a modified periodic risk model in which the periodic risk process is perturbed by a standard Brownian motion.The insurer can invest in multiple risky assets and one risk-free asset and the correlations between the risky assets and the risk process are considered.Optimal strategy is obtained explicitly,which is a function of time and related to the risk process.The effects of market parameters on the optimal strategy are discussed and a numerical example is also given.     

Optimal dividend strategies in the diffusion model with stochastic return on investments

This paper studies the optimal dividend problem in the diffusion model with stochastic return on investments. The insurance company invests its surplus in a financial market. More specially, the authors consider the case of investment in a Black-Scholes market with risky asset such as stock. The classical problem is to find the optimal dividend payment strategy that maximizes the expectation of discounted dividend payment until ruin. Motivated by the idea of Thonhauser and Albrecher (2007), we take the lifetime of the controlled risk process into account, that is, the value function considers both the expectation of discounted dividend payment and the time value of ruin. The authors conclude that the optimal dividend strategy is a barrier strategy for the unbounded dividend payment case and is of threshold type for the bounded dividend payment case.     

索赔到达间隔为几何分布风险模型的破产问题

讨论了索赔到达间隔时间服从几何分布,索赔额分布为一般离散型分布的一类连续时间风险模型的破产问题,先将风险模型纳入PDMP框架,借助于带离散分量的广义生成元的概念得到相关鞅,再利用测度变换理论得到破产概率的一般表达式,有趣的是破产函数不是连续的,而是逐段常值的.     

Complete monotonicity of the probability of ruin and de Finetti’s dividend problem

This paper studies the complete monotonicity of the probability of ruinψin the the classical risk model and the classical risk model that is perturbed by a diffusion.As a byproduct,the authors give an alternative proof to a result on the optimal dividend problem due to LoefFen(2008).     

The Optimal Dividend Barrier in the Perturbed Compound Poisson Risk Model with Randomized Observation Time

This paper considers the dividend problems in the perturbed compound Poisson risk model.Assume that dividends can only be paid at the observation time when the surplus exceeds the barrier level and the excess is paid as dividend.In this paper,integro-differential equations for the expected discounted dividends until ruin and the Laplace transform of ruin time are firstly derived.When the claim is exponentially distributed,explicit expressions for the expected discounted dividends until ruin and the Laplace transform of ruin time are also obtained.Finally,the optimal dividend barrier which maximizes the expected discounted dividends until ruin is given.     

保险公司破产概率的估计及随机模拟

研究人寿保险的破产模型 ,其中保单到达和索赔发生时刻为相互独立的 Poisson流 ,索赔额服从指数分布 .针对此模型给出了 t时刻之前破产概率的一个上界估计 ,并给出了破产概率的随机模拟计算流程和一个具体例子的数值模拟结果.     

兼并多个目标企业的策略选择和时机确定

通过引入兼并成功概率,给出了协同价值大小和协同价值是否实现双重不确定下的单目标企业兼并时机.并把模型扩展到兼并多个目标企业情形,对独立兼并策略和序列兼并策略下的兼并时机进行求解.通过比较两种策略下的兼并阈值和主并企业价值,得到了兼并多个目标企业时的最优兼并策略.由于序列兼并可以获得额外的信息价值,序列兼并策略下的兼并阈值小于独立兼并策略下的兼并阈值,而且存在一段序列兼并区间, 使得序列兼并策略优于独立兼并策略.最后通过数值分析, 揭示了相关系数, 兼并成功概率,主并企业讨价还价能力对兼并阈值和序列兼并区间的影响.     

Optimal investment problem for an insurer and a reinsurer

This paper studies the optimal investment problem for an insurer and a reinsurer. The basic claim process is assumed to follow a Brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer. The insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset. Moreover, the authors consider the correlation between the claim process and the price process of the risky asset. The authors ?rst study the optimization problem of maximizing the expected exponential utility of terminal wealth for the insurer. Then with the optimal reinsurance strategy chosen by the insurer, the authors consider two optimization problems for the reinsurer: The problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the ruin probability. By solving the corresponding Hamilton-Jacobi-Bellman equations, the authors derive the optimal reinsurance and investment strategies, explicitly. Finally, the authors illustrate the equality of the reinsurer's optimal investment strategies under the two cases.     

Upper bound for finite-time ruin probability in a Markov-modulated market

This paper studies the upper bound for finite-time ruin probability of an insurance company which invests its wealth in a stock and a bond. The authors assume that the interest rate of the bond and the volatility of the stock are modulated by a continuous-time stationary Markov chain with finite state. By a pure probabilistic method, the upper bound for the finite-time ruin probability is obtained.     

Minimizing the Risk of Absolute Ruin Under a Diffusion Approximation Model with Reinsurance and Investment

This paper studies the optimization problem with both investment and proportional reinsurance control under the assumption that the surplus process of an insurance entity is represented by a pure diffusion process.The company can buy proportional reinsurance and invest its surplus into a Black-Scholes risky asset and a risk free asset without restrictions.The authors define absolute ruin as that the liminf of the surplus process is negative infinity and propose absolute ruin minimization as the optimization scenario.Applying the HJB method the authors obtain explicit expressions for the minimal absolute ruin function and the associated optimal investment strategy.The authors find that the minimal absolute ruin function here is convex,but not S-shaped investigated by Luo and Taksar(2011).And finally,from behavioral finance point of view,the authors come to the conclusion:It is the restrictions on investment that results in the kink of minimal absolute ruin function.     

远距离支援最优干扰空域规划

针对支援突防作战中远距离支援干扰机最优空域的规划问题,确定了干扰机的配置范围、雷达探测范围,提出了航线安全间隔和有效干扰航段的概念,以有效干扰航段、干扰机数量和干扰机离雷达中心的距离三个参数构建评价函数,建立了远距离支援有源干扰空域规划的模型。该模型具有多约束、非线性的特点,因此采取灰狼优化算法对其求解,为降低在模型求解时算法陷入局部最优的概率,引入非线性调节参数和记忆功能对灰狼优化算法进行改进,继而规划出相应的空域。采用仿真的方式验证模型的合理性和求解算法的有效性,得到了不同决策偏好下的空域。     

保险公司破产模型的进一步研究

引入一个新的概念——标准索赔额，建立一种新的破产模型并给出它的破产概率，从而使得破产概率更具有现实意义，并可作为衡量保险公司金融风险的一个重要指标。     

关于“定期人寿保险中的破产模型”的注记

利用风险理论,对定期人寿保险模型进行了研究,得到了定期人寿保险模型的破产概率的表达式.     

主从型Bertrand价格博弈模型及其动力学分析

基于有限理性策略与适应性策略,构建两寡头企业主从型Bertrand价格博弈模型,并研究该模型的动力学性质。理论分析表明,该模型有一个不稳定的边界不动点和一个局部稳定的纳什平衡点。计算实验证实,采用有限理性策略的企业的价格调整速度较大时会引起两企业价格演化的倍周期分岔现象,并最终导致价格演化的混沌行为。保持较低的价格调节速度,获取纳什均衡利润是两寡头企业价格博弈的最优结果。     

Optimal proportional reinsurance under dependent risks

This paper considers a correlated risk model with thinning-dependence structure.The authors investigate the optimal proportional reinsurance that maximizes the adjustment coefficient and the optimal proportional reinsurance under mean variance principle for the proposed model.The authors derive the optimal solutions and the numerical illustrations to show the impact of the dependence among the classes of business on the optimal reinsurance arrangements.     

基于自适应伪谱法的UCAV低可探测攻击轨迹规划研究

研究无人作战飞机(unmanned combat aerial vehicle,UCAV)对地攻击阶段轨迹规划问题。首先,在综合UCAV的气动力特性、发动机推力特性基础上建立UCAV质点模型和动力学模型,并结合UCAV平台初始条件、机动性以及武器投射条件构建约束条件;针对当前轨迹规划中没有考虑雷达散射截面(radar cross section,RCS)随UCAV姿态角改变而动态变化这一缺陷,建立综合考虑动态RCS的威胁概率和攻击时间的目标函数;然后利用可变低阶自适应伪谱法求得攻击轨迹最优解。对时间最短、RCS固定和考虑动态RCS 3种情况进行仿真。结果表明,考虑动态RCS时,UCAV将根据威胁进行轨迹和姿态调整,极大减小了被敌方威胁捕获的概率。该算法能够提供规划轨迹的高精度状态和控制量信息,有利于实现攻击过程的高精度精细规划控制。     

两类相关索赔模型下破产概率的若干结果

研究了两类相关风险模型中生存概率φ(u)的问题,将其中一个风险由一个复合Poisson过程推广到了广义复合Poisson过程,求出了索赔额分布为指数分布时生存概率的明确表达式,并研究了此模型下索赔额分布重尾时,φ(u)的一个尾等价关系.