S型效用下比例再保险的最优投资策略

本文引入了行为金融学中的损失厌恶概念,研究考虑损失厌恶时保险公司的最优投资再保险问题.在损失厌恶下,保险公司面对盈利时是风险厌恶者,而遭受损失时转为风险追求者,因此本文采用S型效用函数,并以终端财富的效用最大化为目标求解保险公司的最优策略.假定保险公司的盈余过程服从经典的Cramer-Lundberg模型,可将资产投资于一种无风险资产和一种服从几何布朗运动的风险资产,且可以通过向再保险公司购买比例再保险来分散风险、稳定经营.通过构造鞅过程,运用鞅方法和拉格朗日对偶法求解出最优策略与最优财富.最后进行数值分析,更加直观地解释了各经济参数对财富值和投资策略的影响.     

仿射利率模型下的最优再保险-投资策略

研究仿射利率模型下的最优投资与再保险策略问题。保险公司通过购买比例再保险来分担公司风险,并将财富投资于金融市场。金融市场包括一种无风险资产、一种风险资产和一种零息票债券,其中无风险利率是服从仿射利率模型的随机过程,盈余过程遵循带漂移的布朗运动。文章应用动态规划原理得到了指数效用下最优再保险-投资策略的显式解,并给出数值算例分析了市场参数对最优再保险-投资策略的影响。     

保险公司和再保险公司的最优投资策略

假设保险公司和再保险公司面临的赔付过程是带漂移的布朗运动.保险公司可以向再保险公司购买比例再保险,两公司均可以投资于一种无风险资产和一种价格服从几何布朗运动模型的风险资产,并以到期财富的期望效用最大化为目标.根据随机控制理论建立相应的HJB方程并求解,分别得到了保险公司与再保险公司的最优投资和再保险策略的解析解,并分析了同时满足双方利益的再保险策略.最后通过数值实例分析了各模型参数对最优策略的影响.     

考虑基准资产的多阶段时间一致投资-再保险策略优化

区别于其它机构投资者,保险公司将面临由保险索赔和证券投资所带来的双重风险。因此,在实际投资过程中,保险公司往往会将某种具有相对稳定收益的资产或组合作为基准,以期为其带来更加持续稳定的收益。然而,已有相关研究多数在连续框架下讨论保险公司的最优投资-再保险的策略优化问题,且没有考虑基准资产对投资-再保险策略的影响。本文首次在多阶段均值-方差框架下,将基准资产考虑到保险公司的投资-再保险策略优化当中。运用倒向递推法分别求出保险公司的时间一致投资-再保险策略和相应值函数的解析表达式。数值分析表明:(1)在给定风险厌恶系数下,相比于不考虑基准资产的投资-再保险策略,基准资产的考虑会促使决策者愿意在投资过程中承担更大的风险;(2)考虑基准的投资-再保险策略能够有效地跟踪基准的收益过程。此外,样本外评价结果进一步验证了考虑基准资产的时间一致投资策略的确可以为投资者带来更多的投资回报。     

含有期权的最优投资与比例再保险策略

在Black-Scholes模型假设的市场条件下,研究了保险公司投资对象含有欧式看涨期权的情形下,进行投资和比例再保险的策略问题.以保险公司到期财富效用最大化为目标,运用动态规划原理得到了最优值函数满足的HJB方程,得到了包含期权在内的资产最优投资策略和比例再保险策略的显式解,并证明了解的验证定理.最后分析了不同参数对模型策略的影响.     

考虑模糊厌恶和时滞效应的随机微分投资与再保险策略

金融市场中,保险公司之间存在市场竞争,他们不仅追求自身财富的最大化,同时还关注与竞争对手的财富比较.将模糊厌恶和时滞效应引入到非零和投资与比例再保险策略问题中,研究模糊厌恶水平和时滞效应对互相竞争的保险公司均衡投资和再保险策略的影响.针对经典CramerLundberg模型的近似风险扩散过程,运用微分博弈理论和随机最优控制理论,通过求解相应的HJB方程,得到了模糊厌恶和时滞效应下基于指数效用的均衡投资与再保险策略以及值函数的显式解.最后结合数值算例仿真分析了模型参数变动对均衡策略的影响.实证结果表明:是否考虑模糊厌恶和时滞信息将大大影响最终的均衡再保险策略和最优投资策略.保险公司对风险的模糊厌恶越高,越多地考虑较早时间的财富值,在投资行为上就越趋于谨慎理性;而保险公司越看重与对手之间的竞争,则越趋于冒险投资.     

随机利率下的再保险与投资策略

假设保险公司在考虑比例再保险下,并将盈余资金在无风险资产和风险型资产中进行配置,考虑了利率的随机性,建立了求解相应的HJB方程,并针对CARA效用函数求解HJB方程,得出最优的再保险比例和在各类资产中的投资比例。     

基于偿付能力的最优再保险策略

采用最大索赔再保费定价原则,结合VaR、CTE、TV三种风险测度方法,通过研究最小化偿付不足风险的概率、期望损失以及均方期望超额损失等再保险问题,得到相应的最优再保险策略,并结合案例对各种最优策略进行静态分析.研究发现,当偿付能力基于VaR或者CTE时,最优的再保险策略是去尾停止损失再保险,这说明原保险公司此时应该更注重对中等巨额损失的保障,而没有动力去保障极值损失;当偿付能力基于TV时,最优策略是带限额的停止损失再保险,此时,保险公司为了保证经营的稳定性,势必会将一部分极值损失分保.     

具有合作与竞争的鲁棒最优再保险合同

本文研究了n个合作的保险人与一个再保险人之间竞争下的最优再保险合同制定问题.再保险合同由索赔风险分担策略和再保险价格构成. n个保险人完全相信各自的盈余过程,而再保险人认为每个保险人的盈余过程存在不确定性.每个保险人的目标是,寻找最优的索赔风险分担策略最大化他的终值财富的均值同时最小化其方差.再保险人的目标是,在盈余过程出现最坏情形下,寻找鲁棒最优再保险价格最大化他的终值财富的均值同时最小化其方差.在Stackelberg博弈框架下,通过使用随机控制和随机动态规划技术得到了最优的索赔风险分担策略和再保险价格的显式解,进而得到了最优再保险合同的显式解.最终,通过数值实验解释了模型参数对所得理论结果的影响,得到了一些新的再保险启示.     

VaR下拥有两类业务的最优再保险投资策略

允许保险资金在资本市场上进行投资的前提下，以终期财富最大化为目标，通过VaR进行风险测度，以原保险公司最大风险量为限制条件，研究两种保险业务风险相互独立和风险相依两种情况下的比例再保险的最优投资策略。通过对比研究发现：终期财富和最优自留比例由最大风险量、承保和投资组合收益的均值与方差共同决定；最优自留比例的大小可以为保费准则选择提供决策依据；相较于风险相互独立情况，由共同影响因子引起的索赔次数将影响风险相依的两种业务的最优自留比例。     

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.     

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 multi-asset investment with no-shorting constraint under mean-variance criterion for an insurer

This paper considers the optimal investment strategy for an insurer under the criterion of mean-variance. The risk process is a compound Poisson process and the insurer can invest in a risk-free asset and multiple risky assets. This paper obtains the optimal investment policy using the stochastic linear quadratic (LQ) control theory with no-shorting constraint. Then the efficient strategy (optimal investment strategy) and efficient frontier are derived explicitly by a verification theorem with the viscosity solution of Hamilton-Jacobi-Bellman (HJB) equation.     

Optimal reinsurance and investment strategies for insurers with regime-switching and state-dependent utility function

This paper considers a proportional reinsurance-investment problem and an excess-of-loss reinsurance-investment problem for an insurer, where price processes of the risky assets and wealth process of the insurer are both described by Markovian regime switching. The target of the insurer is assumed to maximize the expected exponential utility from her terminal wealth with a state-dependent utility function. By employing the dynamic programming approach, the optimal value functions and the optimal reinsurance-investment strategies are derived. In addition, the impact of some parameters on the optimal strategies and the optimal value functions is analyzed, and lots of interesting results are discovered, such as the conclusion that excess-of-loss reinsurance is better than proportional reinsurance is not held in the regime-switching jump-diffusion model.     

Optimal investment with multiple risky assets under short-selling prohibition in a periodic environment

In this paper,the surplus process is assumed to be a periodic risk model and the insurer is allowed to invest in multiple risky assets described by the Black-Scholes market model.Under short-selling prohibition,the authors consider the optimal investment from an insurer’s point of view by maximizing the adjustment coefficient and the expected exponential utility of wealth at one period, respectively.It is shown that the optimal strategies of both of optimization problems are to invest a fixed amount of money in each risky asset.     

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.     

仿射利率模型下确定缴费型养老金的最优投资

论文研究了仿射利率模型(包括CIR模型和Vasicek模型) 下的确定缴费型养老金的最优投资问题. 在模型中, 养老基金被允许投资于一种无风险资产、一种零息债券和一种风险资产. 通过运用HJB方程、Legendre转换和对偶理论, 分别找到对CRRA和CARA效用函数的显性解.     

跳跃扩散市场的最优保险投资决策

假定保险公司的盈余为Crámer-Lundberg过程,保险公司的投资市场是由一个无风险债券和n个风险证券构成的资本市场.风险证券的价格服从带跳的扩散过程.在均值-方差准则下通过最优控制原理来研究保险公司的最优投资策略选择问题.得到了最优 投资策略和有效边界的显式表达式.与在最大化最终财富期望效用准则下得到的最优投资策略不同, 所得到的最优策略依赖保险索赔 过程的所有因素.最后分析了最优投资策略随保险索赔过程各个因素变化的动态性质.     

信用债券型基金的最优资产配置策略

对信用债券型基金的最优资产配置策略进行了研究。利用简约化模型对信用债券进行定价,并给出其价格的动态过程,通过随机控制方法求出了最优策略的解析解,揭示了跳跃风险溢价对最优策略的影响。结果表明:只有当信用债券的跳跃风险溢价大于1,即市场对跳跃风险进行风险补偿时,投资基金才会持有信用债券;否则,投资基金对信用债券的最优投资为零。