基于索赔相依的时滞均衡投资与再保险策略

本文研究保险公司的最优投资与再保险问题.假设再保险种类是比例再保险,未来索赔与历史索赔是相关的.此外,风险资产的价格过程由常方差弹性模型来描述,并且在财富过程中考虑了财富的时滞效应.在均值-方差优化准则下,本文给出了最优均衡投资和比例再保险策略及值函数的显式解.最后,通过数值分析,讨论了模型主要参数对最优策略的影响.本文所提模型及所获结果是对文献中已有研究成果的推广.     

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.     

Ornstein-Uhlenbeck模型的最优再保险和投资

研究了均值-方差准则下保险公司的最优再保险和投资.保险公司的盈余满足CramerLundberg风险模型;为了减小风险,它可以采取再保险;同时为了增加财富,它可以进行投资.风险资产通过Ornstein-Uhlenbeck(O-U)模型来描述.研究目标是:求得最优再保险策略、最优投资策略及有效边界的显式解.应用It公式和线性-二次控制理论求解了该问题.通过文章研究不仅丰富和发展了策略选择问题,也对保险公司进行再保险和投资具有一定的指导意义.     

基于均值-方差准则的保险公司最优投资策略

研究了保险公司在均值-方差准则下的最优投资问题,其中保险公司的盈余过程由带随机扰动的Cramer-Lundberg模型刻画,而且保险公司可将其盈余投资于无风险资产和一种风险资产.利用随机动态规划方法,通过求解相应的HJB方程,得到了均值方差模型的最优投资策略和有效前沿.最后,给出了数值算例说明扰动项对有效前沿的影响.     

在不允许卖空条件下的最优比例再保险投资

假设保险公司的盈余过程服从一个带扰动项的布朗运动,保险公司可以投资一个无风险资产和n个风险资产,还可以购买比例再保险,并且风险市场是不允许卖空的.本文在均值一方差优化准则下研究保险公司的最优投资一再保策略选择问题,利用LQ随机控制方法求解模型,得到了保险公司的最优组合投资策略的解析和保险公司投资的有效投资边界的解析表达...     

方差保费原则下具有违约风险的均值-方差保险者的时间一致最优投资和再保险问题（英文）

本文研究在均值-方差准则下保险者的最优投资再保险策略问题,其中保险者可以投资到无风险资产,股票和违约债券上,股票服从Heston模型.保险者可以购买比例再保险或者得到新的保险业务,特别地,保险和再保险的保费通过方差保费原则来计算.通过使用博弈论方法,我们分别解决了违约前和违约后的扩展的HJB方程并且得到了相应的时间一致最优投资再保险策略表达式.最后,我们用数值例子来说明模型参数对最优策略的影响.     

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.     

Markov调节中基于时滞和相依风险模型的最优再保险与投资

本文研究保险公司在Markov调节下基于时滞及相依风险模型的最优再保险与最优投资问题,其中市场被划分为有限个状态,一些重要的参数随着市场状态的转换而变化.假设保险公司的盈余过程由复合Poisson过程描述,而风险资产的价格过程由几何跳扩散模型刻画,并且假设这两个跳过程是相依的.以最大化终端财富值的均值-方差效用为目标,在博弈论框架下,利用随机控制理论和相应的广义Hamilton-Jacobi-Bellman(HJB)方程,本文得到最优策略和值函数的显式表达,并证明解的存在性和唯一性.最后,通过一些数值实例,验证所得结论的正确性,并探讨一些重要参数对最优策略的影响.     

具有随机利率、随机变差的最优投资和联合比例-超额损失再保险

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.     

Poisson-Geometric模型下时间一致的最优再保险-投资策略选择

本文研究Poisson-Geometric模型下,时间一致的再保险-投资策略选择问题.在风险模型中,理赔发生次数用Poisson-Geometric过程描述,保险公司在进行再保险时,按照方差值原理计算再保险的保费.保险人在金融市场上投资时,风险资产满足带跳的随机微分方程.保险人的目标是,选择一个时间一致的再保险-投资策略,最大化终止时刻财富的均值同时最小化其方差.通过使用随机控制理论,求得时间一致的再保险-投资策略以及值函数的显式解.最后分析结果的经济意义,并通过数值计算,解释了模型参数对最优策略的影响.     

基于均值-VaR的投资组合最优化

利用均值-VaR方法,提出了有交易费用存在时的最优投资组合模型。通过求解均值-方差模型来研究均值-VaR模型的有效前沿,并指出在收益率的分布为正态分布的假设下,均值-VaR模型的有效集是均值-方差有效前沿的子集。有关全局最小VaR的存在性的分析显示在选择VaR的置信水平时必须非常小心。最后给出了应用均值-VaR模型的实例分析。     

均值-VaR模型的一种新解法：鞍点近似、遗传算法

以均值度量收益,方差度量风险的均值.方差模型,广泛应用于资产组合优化.随着对金融风险度量方法研究的不断深入,VaR作为一种简便、易于理解的风险度量方法,在金融企业中得到日益广泛的应用.本文用VaR代替均值-方差模型中的方差,构建了均值-VaR模型应用干投资组合优化.均值-VaR模型是非线性规划,仅当VaR满足凸性和可微性的前提下,满足库恩-塔克条件的解才是全局最优解.本文在CreditRisk+框架下,提出一个在不允许卖空条件下,不需对VaR的性质做出前提假定的新解法:将鞍点近似法用于计算VaR,在资产头寸与VaR之间建立起函数关系,采用遗传算法寻找模型的近似最优解.并用一个债券组合说明该方法的有效性。     

Open-loop equilibrium reinsurance-investment strategy under mean–variance criterion with stochastic volatility

This paper investigates the open-loop equilibrium reinsurance-investment (RI) strategy under general stochastic volatility (SV) models. We resolve difficulties arising from the unbounded volatility process and the non-negativity constraint on the reinsurance strategy. The resolution enables us to derive the existence and uniqueness result for the time-consistent mean variance RI policy under both situations of constant and state-dependent risk aversions. We apply the general framework to popular SV models including the Heston, the 3/2 and the Hull–White models. Closed-form solutions are obtained for the aforementioned models under constant risk aversion, and the non-leveraged models under state-dependent risk aversion.     

Portfolio selection problem with multiple risky assets under the constant elasticity of variance model

This paper focuses on the constant elasticity of variance (CEV) model for studying the utility maximization portfolio selection problem with multiple risky assets and a risk-free asset. The Hamilton-Jacobi-Bellman (HJB) equation associated with the portfolio optimization problem is established. By applying a power transform and a variable change technique, we derive the explicit solution for the constant absolute risk aversion (CARA) utility function when the elasticity coefficient is −1 or 0. In order to obtain a general optimal strategy for all values of the elasticity coefficient, we propose a model with two risky assets and one risk-free asset and solve it under a given assumption. Furthermore, we analyze the properties of the optimal strategies and discuss the effects of market parameters on the optimal strategies. Finally, a numerical simulation is presented to illustrate the similarities and differences between the results of the two models proposed in this paper.     

Optimal consumption and investment strategies with liquidity risk and lifetime uncertainty for Markov regime-switching jump diffusion models

In this paper, we consider the optimal consumption and investment strategies for households throughout their lifetime. Risks such as the illiquidity of assets, abrupt changes of market states, and lifetime uncertainty are considered. Taking the effects of heritage into account, investors are willing to limit their current consumption in exchange for greater wealth at their death, because they can take advantage of the higher expected returns of illiquid assets. Further, we model the liquidity risks in an illiquid market state by introducing frozen periods with uncertain lengths, during which investors cannot continuously rebalance their portfolios between different types of assets. In liquid market, investors can continuously remix their investment portfolios. In addition, a Markov regime-switching process is introduced to describe the changes in the market’s states. Jumps, classified as either moderate or severe, are jointly investigated with liquidity risks. Explicit forms of the optimal consumption and investment strategies are developed using the dynamic programming principle. Markov chain approximation methods are adopted to obtain the value function. Numerical examples demonstrate that the liquidity of assets and market states have significant effects on optimal consumption and investment strategies in various scenarios.     

A Mean-variance Problem in the Constant Elasticity of Variance (CEV) Mo del

In this paper, we focus on a constant elasticity of variance (CEV) model and want to find its optimal strategies for a mean-variance problem under two con-strained controls: reinsurance/new business an...     

Exponential Bounds for Ruin Probability in Two Moving Average Risk Models with Constant Interest Rate

The authors consider two discrete-time insurance risk models. Two moving average risk models are introduced to model the surplus process, and the probabilities of ruin are examined in models with a constant interest force. Exponential bounds for ruin probabilities of an infinite time horizon are derived by the martingale method.     

HARVESTING PROCEDURES WITH MANAGEMENT POLICY IN ITERATIVE DENSITY-DEPENDENT POPULATION MODELS

This paper analyzes harvesting in simple one species iterative density-dependent population models. Several harvest management policies are considered, including a constant effort policy, an on-off constant harvest policy, and several policies that include protective strategies. Results for quadratic, Ricker, and Beverton-Holt growth functions are contrasted. It is found that even for the Beverton-Holt case, there are parameter regions where periodic or chaotic behavior can occur under certain harvest policies. In fact, regions of stability and irregularity can alternate.     

For what trading strategies is the tax payment stream of infinite variation?

For an Itô asset price process and under quite mild structural assumptions, we show that the accumulated payments of a linear tax on trading gains are of infinite variation if the quadratic covariation of the trading strategy and the asset price is negative. By contrast, if the strategy is a smooth function of the asset price and some finite variation processes with positive partial derivative with respect to the price variable, then accumulated tax payments are of finite variation. An interesting example are constant proportion portfolio insurance (CPPI) strategies which we extend to models with capital gains taxes. The associated tax payment stream is of finite variation if the tax-adjusted constant multiple of the cushion which is invested in the risky asset is bigger or equal to one. Otherwise, it is of infinite variation.     

组合调整频率会影响投资者的回报率么?——基于分析师股票推荐的投资策略研究

利用巨灵数据库的分析师评级数据,从投资者角度建立动态组合,检验了按每日、每周、每两周、每月、每季度头寸调整频率后的超额收益,研究发现:"买入"评级组合在各种头寸调整频率策略下都获得了超越市场指数的超额回报率,其中按每周频率进行头寸调整策略获得的市场调整后平均超额回报率最高,按三个月频率进行头寸调整策略获得的市场调整后平均超额回报率最低。投资者在面对分析师一致认为"买入"评级股票时,可按照每周更新的频率构建组合,以获取较高的超额回报率。投资者如果按季度调整频率来卖出股票可能会错失投资机会,卖掉的股票很可能会跑赢市场,投资者可按每两周或每四周的频率调整投资组合中的股票,卖出负面推荐评级"减持/卖出"股票,降低投资亏损。