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.     

最优再保险及投资组合策略问题北大核心

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.     

风险相依下再保险双方的联合最优再保险问题

结合保险人和再保险人的共同利益,研究了具有两类相依险种风险模型下的最优再保险问题.假定再保险公司采用方差保费原理收取保费,利用复合Poisson模型和扩散逼近模型两种方式去刻画保险公司和再保险公司的资本盈余过程,在期望效用最大准则下,证明了最优再保险策略的存在性和唯一性,通过求解Hamilton-Jacobi-Bellman（HJB）方程,得到了两种模型下相应的最优再保险策略及值函数的明晰解答,并给出了数值算例及分析.     

风险相依下再保险双方的联合最优再保险问题

结合保险人和再保险人的共同利益,研究了具有两类相依险种风险模型下的最优再保险问题.假定再保险公司采用方差保费原理收取保费,利用复合Poisson模型和扩散逼近模型两种方式去刻画保险公司和再保险公司的资本盈余过程,在期望效用最大准则下,证明了最优再保险策略的存在性和唯一性,通过求解Hamilton-Jacobi-Bellman(HJB)方程,得到了两种模型下相应的最优再保险策略及值函数的明晰解答,并给出了数值算例及分析.     

两类相依保险业务下基于竞争的最优再保险策略

在再保险合同制定中,保险公司与再保险公司之间是竞争的.利用相对业绩,本文量化了这种竞争.进而假设保险公司从事两类相依保险业务,在竞争下,得到了保险公司的相对财富过程.保险公司的目标是,寻找最优时间一致的再保险策略最大化终端财富的均值同时最小化其方差.通过使用随机分析和随机控制理论,求得了最优时间一致的再保险策略和值函数的显式解,并从理论方面解释了最优解的保险和经济意义.最终,通过数值实验分析了模型参数对最优时间一致再保险策略的影响,比较了两类特殊情形与一般情形下最优再保险策略之间的关系.通过本文的研究得到了一些新的发现,研究结果可以更合理地指导保险公司的再保险决策.     

连续时间模型下的动态随机合作再保险策略

如何通过选择再保险策略以最大化保险公司的终端期望效用是保险精算领域中的一个热门研究话题.这个问题在单期离散模型下已经有了很好的研究结果.本文首次考虑了连续时间模型下的最优动态合作再保险问题.基于互惠的再保险概念和指数效用函数,本文引入了博弈论中的Pareto最优概念,给出了含有Pareto最优合作再保险策略的核的界定方法并证明此核是非空的.通过实例,验证了合作再保险博弈的核的非空性,并且得出了在两家保险公司的情形下(保险公司和再保险公司),Pareto最优合作再保险策略是比例再保险策略.     

最优多期比例再保险策略的必要条件

研究最小化保险公司破产概率的最优多期比例再保险策略,给出了保险公司最小破产概率的一个递归表达式,证明了可用动态规划方法求解此类问题.在此基础上,我们推导出最优多期比例再保险策略的几个必要条件.     

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.     

基于风险调整资本收益率下的最优再保险策略

风险调整资本收益率是一个用来描述赚取收益所承担风险的重要指标,是衡量风险调整后的财务绩效的一个有效工具,在银行业中得到广泛采用。近年来,在保险公司的再保险业务中,也越来越多地采用风险调整资本收益率这一指标来衡量收益和风险。本文重新考虑了有再保险控制下的风险调整资本收益率,并得到:在一般再保险自留函数下,我们证明了分层再保险策略是最优再保险形式;进一步,我们获得了最优再保险分层水平及最优风险调整资本收益率;最后,我们也给出了算例及数值分析。     

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Hamilton-Jacobi-Bellman方程求解保险业最优投资策略

在经典复合泊松模型中,保险公司将资金投入一个风险投资过程和一个无风险投资过程.当索赔的分布确定后,运用随机控制中的HJB方程最小化保险公司的破产概率,在已知投资规模或投资组合的情况下求解二者中的另一项,进而得到最优投资策略并讨论各种策略的运用对破产概率的影响.解决保险公司的投资资金分配问题,在实际应用中具有一定的参考价值.     

Optimal control problem for an insurance surplus model with debt liability

For an insurance company with a debt liability, they could make some management actions, such as reinsurance, paying dividends, and capital injection, to balance the profitability and financial bankruptcy. Our objective is to determine risk retention rate, dividend, and capital injection strategy so as to maximize the expected discounted dividends minus the discounted cost of capital injection until the time of ruin. We assume that the dividend payments and capital injection should occur with both fixed and proportional costs. We obtain explicit expressions of the optimal value functions as well as the corresponding optimal joint strategies by routine procedures in a comprehensive basic model using a new technique to solve the related equations. Our results show that whether recapitalizing is profitable or not depends on the costs of capital raising and that the firm injects capital only when the reserves are zero and recapitalizes to the optimal reserves level if the cost of external capital is low. Copyright © 2013 John Wiley & Sons, Ltd.     

A doubly optimal stopping of a risk process (Poster Presentation)

Problems which lead to an optimal stopping of a risk process are considered. Let an insurance company be endowed with an initial capital a > 0, receive insurance premiums and pay out successive claims. The losses occur according to renewal process. At any moment the company may broaden or narrow down the offer, what entails the change of the parameters. These changes concern the rate of income, the intensity of renewal process and the distribution of claims. The model of the risk process with two types of claims stream is considered. After the change the management wants to know the moment of the maximal value of the capital assets. Our goal is to find two optimal stopping times: the best moment of change the parameters and the moment of maximal value of the capital assets. A dynamic programming method to calculate the expected capital at that times is used. Based on the model which combine two types of risk the model of reinsurance with two firms is formulated. In this case the aim is to find for the firms the equilibrium strategy. The equilibrium is constructed in class of strategies driven by their risks. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

含不动产项目的保险公司再保险-投资策略

站在保险公司管理者的角度, 考虑存在不动产项目投资机会时保险公司的再保险--投资策略问题. 假定保险公司可以投资于不动产项目、风险证券和无风险证券, 并通过比例再保险控制风险, 目标是最小化保险公司破产概率并求得相应最佳策略, 包括: 不动产项目投资时机、 再保险比例以及投资于风险证券的金额. 运用混合随机控制-最优停时方法, 得到最优值函数及最佳策略的显式解. 结果表明, 当且仅当其盈余资金多于某一水平(称为投资阈值)时保险公司投资于不动产项目. 进一步的数值算例分析表明: (a)~不动产项目投资的阈值主要受项目收益率影响而与投资金额无明显关系, 收益率越高则投资阈值越低; (b)~市场环境较好(牛市)时项目的投资阈值降低; 反之, 当市场环境较差(熊市)时投资阈值提高.     

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??Under inflation influence, this paper investigate a stochastic differential game with reinsurance and investment. Insurance company chose a strategy to minimizing the variance of the final wealth, and the financial markets as a game ``virtual hand' chosen a probability measure represents the economic ``environment' to maximize the variance of the final wealth. Through this double game between the insurance companies and the financial markets, get optimal portfolio strategies. When investing, we consider inflation, the method of dealing with inflation is: Firstly, the inflation is converted to the risky assets, and then constructs the wealth process. Through change the original based on the mean-variance criteria stochastic differential game into unrestricted cases, then application linear-quadratic control theory obtain optimal reinsurance strategy and investment strategy and optimal market strategy as well as the closed form expression of efficient frontier are obtained; finally get reinsurance strategy and optimal investment strategy and optimal market strategy as well as the closed form expression of efficient frontier for the original stochastic differential game.     

Optimal investment and reinsurance of an insurer with model uncertainty

We introduce a novel approach to optimal investment–reinsurance problems of an insurance company facing model uncertainty via a game theoretic approach. The insurance company invests in a capital market index whose dynamics follow a geometric Brownian motion. The risk process of the company is governed by either a compound Poisson process or its diffusion approximation. The company can also transfer a certain proportion of the insurance risk to a reinsurance company by purchasing reinsurance. The optimal investment–reinsurance problems with model uncertainty are formulated as two-player, zero-sum, stochastic differential games between the insurance company and the market. We provide verification theorems for the Hamilton–Jacobi–Bellman–Isaacs (HJBI) solutions to the optimal investment–reinsurance problems and derive closed-form solutions to the problems.     

On optimal dividends with exponential and linear penalty payments

We study the optimal dividend problem where the surplus process of an insurance company is modelled by a diffusion process. The insurer is not ruined when the surplus becomes negative, but penalty payments occur, depending on the level of the surplus. The penalty payments shall avoid that losses can rise above any number and can be seen as a preference measure or costs for negative capital. As examples, exponential and linear penalty payments are considered. It turns out that a barrier dividend strategy is optimal.     

Optimal dividend and investing control of an insurance company with higher solvency constraints

This paper considers the optimal control problem of a large insurance company under a fixed insolvency probability. The company controls proportional reinsurance rate, dividend pay-outs and investing process to maximize the expected present value of the dividend pay-outs until the time of bankruptcy. This paper aims at describing the optimal return function as well as the optimal policy. As a by-product, the paper theoretically sets a risk-based capital standard to ensure the capital requirement that can cover the total risk.     

Complete discounted cash flow valuation

This paper concerns discounted cash flow valuation of a company. When the company is in trouble, the owners have an option to provide it with a new capital; otherwise it is liquidated. In the absence of capital outflows and inflows, the company’s own funds are modelled by a spectrally negative Lévy process. Within this framework, we look for a strategy of dividend payments and capital injections which maximizes the firm’s value. We provide an optimal strategy as well as the corresponding valuation formula. Illustrative examples are given.     

Optimal dividend and investing control of an insurance company with higher solvency constraints

This paper considers the optimal control problem of a large insurance company under a fixed insolvency probability. The company controls proportional reinsurance rate, dividend pay-outs and investing process to maximize the expected present value of the dividend pay-outs until the time of bankruptcy. This paper aims at describing the optimal return function as well as the optimal policy. As a by-product, the paper theoretically sets a risk-based capital standard to ensure the capital requirement that can cover the total risk.