免赔额保险公平定价的期权博弈分析

传统保险定价实质上是供给方定价,忽视了保险契约是保险人和投保人双方互动决策的结果.另一方面,保单具有或有权益的性质,这使得近年来金融定价方法得以引入到保险定价中,以反映风险和回报之间的长期均衡关系.借助期权博弈框架引入博弈论和期权定价理论,分析了免赔额保险的公平定价问题,给出了基本模型和扩展模型两种情形下博弈均衡结果,即保单的无套利价值,并发现在扩展模型情形下,投保人的最优投保策略和均衡保险合同均发生变化.     

动态资产份额定价理论模型

运用倒向随机微分方程数学方法 ,建立了动态资产份额定价理论模型 .这一模型是资产份额定价法的改进 .求解模型得到动态资产份额定价理论公式 ,并得出结论 :资产份额定价公式完全可以作为特例 ,以离散时间意义和在不考虑动态投资的情况下 ,由动态资产份额定价理论公式得到 .     

不完全市场的保险定价研究

完全市场上的保险定价问题是人们比较熟悉的研究内容,但它不符合市场实际.本文在不完全市场上研究保险定价的问题.通过对累积保险损失的分析,建立在累积赌付下的保险定价模型;基于对一个无风险资产和有限多个风险资产的投资,建立保险投资定价模型.通过变形,得到相应的保险价格的倒向随机微分方程,并利用倒向随机微分方程的理论和方法,得到了相应的保险价格公式.最后,给出释例进行了分析.本文的研究,不用考虑死亡率、损失的概率分布等因素,为保险定价提供了新的思路,丰富了有限的保险定价方法.     

基于投资的我国再保险预测性定价新探讨

从系统的观点出发,把保险公司的赔付情况与投资收益结合,对非比例再保险建立在一类在较弱的市场假设条件下进行投资的线性正倒向随机微分方程的改进模型.根据一类特殊线性倒向随机微分方程的显式解,加入时间序列预测方法,给出了基于投资的非比例再保险定价公式,为保险公司厘定非比例再保险的保费提供新的可行性方法.     

与汇率挂钩的外币存款产品定价

本文考虑具有比例支付交易费用下与汇率挂钩的外币存款产品定价问题.利用无套利原理和Δ-对冲的方法,建立了与汇率挂钩的外币存款产品合约的数学模型,采用偏微分方程方法,获得相应的解定价表达式.     

基于投资的再保险定价公式

从系统的观点出发,把保险公司的赔付情况与投资收益相结合,对比例再保险和超额损失再保险,建立了在投资背景下它们应满足的线性正倒向随机微分方程.根据一类特殊线性倒向随机微分方程的显式解,给出了基于投资的再保险定价公式,为保险公司厘订再保险保费提供了新的方法.     

不允许卖空和VaR约束下分红型寿险合同的最优资产配置——基于保险人和被保险人的双重视角

基于保险人和被保险人双重视角出发,研究了在不允许卖空和两个VaR约束下,发行分红型寿险合同的保险人的最优投资问题.该研究对既需在偿二代监管下最大化保险人终端财富的期望效用,又需提供给投保人最低到期保障和分红的保险人具有很好的指导意义.利用对偶控制方法和凹化技巧解决了该优化问题,给出了最优终端财富的封闭解.数值结果显示了从保险人和被保险人双方角度出发所考虑的两个VaR约束比从保险人或被保险人任一方角度出发所考虑的单个VaR约束更能够严格改进经济状态不好时的风险管理,达到降低道德风险的作用.     

倒向随机方程期权定价模型的一类随机算法

期权定价问题可以转化为对倒向随机微分方程的求解,进而转化为对相应抛物型偏微分方程的求解.为了求解与倒向随机微分方程相应的二阶拟线性抛物型微分方程初值问题,引入一类新的随机算法-分层方法取代传统的确定性数值算法.这种数值方法理论上是通过弱显式欧拉法,离散其相应随机系统解的概率表示而得到.该随机算法的收敛性在文中得到证明,其稳定性是自然的.并构造了易于数值实现的基于插值的算法,实证研究说明这种算法能很好地提供期权定价模型的数值模拟.     

外汇期权的多维跳-扩散模型

本文建立了外汇期权的多维跳-扩散模型,在此模型下将外汇欧式未定权益的定价问题归结为一类倒向随机微分方程的求解问题,证明了这类倒向随机微分方程适应解的存在唯一性问题,并给出了一个关于外汇欧式未定权益的定价公式.     

基于近似对冲跳跃风险的美式看跌期权定价及数值解法研究

考虑了基于近似对冲跳跃风险的美式看跌期权定价问题。首先,运用近似对冲跳跃风险、广义It 公式及无套利原理,得到了跳-扩散过程下的期权定价模型及期权价格所满足的偏微分方程。然后建立了美式看跌期权定价模型的隐式差分近似格式,并且证明了该差分格式具有的相容性、适定性、稳定性和收敛性。最后,数值实验表明,用本文方法为跳-扩散模型中的美式期权定价是可行的和有效的。     

基于不确定理论的风险中性测度及其在欧式期权定价中的应用

首先运用不确定理论推导了相应的不确定风险中性测度,修正了已有文献中涨跌期权不满足无套利原则的问题.然后将所得的风险中性测度用于欧式看涨和看跌期权的定价,并验证了涨跌期权价格之间的平价关系.最后研究了一类利差期权的定价问题,结合定义的风险中性测度给出了期权的定价公式.所推导的不确定风险中性测度与经典的无套利原则相吻合,而且考虑到了问题描述过程中存在的不精确性,弥补了单纯依赖随机理论的不足,可广泛地应用于金融衍生品的定价过程,为投资分析提供一定的理论依据.     

Optimal investment,consumption and proportional reinsurance under model uncertainty

This paper considers the optimal investment, consumption and proportional reinsurance strategies for an insurer under model uncertainty. The surplus process of the insurer before investment and consumption is assumed to be a general jump–diffusion process. The financial market consists of one risk-free asset and one risky asset whose price process is also a general jump–diffusion process. We transform the problem equivalently into a two-person zero-sum forward–backward stochastic differential game driven by two-dimensional Lévy noises. The maximum principles for a general form of this game are established to solve our problem. Some special interesting cases are studied by using Malliavin calculus so as to give explicit expressions of the optimal strategies.     

The Pricing of Deposit Insurance Considering Regulatory Capital and Bankruptcy Cost

We develop a deposit insurance pricing model that explicitly considers regulatory capital and bankruptcy costs. Based on the pricing deposit insurance model, we calculate the deposit insurance premiums of China's 16 listed banks with time span of 2011 to 2017 in this paper. The results demonstrate that the deposit insurance premiums of state-owned banks is lower than joint-stock commercial banks and city commercial banks, however, the deposit insurance premiums of joint-stock commercial banks is higher than city commercial banks. Numerical simulation shows that, ceteris paribus, the value of deposit insurance decreases with regulatory capital ratios and the insured deposits ratios, but it increases with interest rate and bankruptcy costs.     

A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications

In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward–backward stochastic differential equations with jumps. First, we prove a sufficient maximum principle for nonzero-sum stochastic differential games problems and obtain equilibrium point for such games. Second, we prove an equivalent maximum principle for nonzero-sum stochastic differential games. The zero-sum stochastic differential games equivalent maximum principle is then obtained as a corollary. We apply the obtained results to study a problem of robust utility maximization under a relative entropy penalty and to find optimal investment of an insurance firm under model uncertainty.     

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??We develop a deposit insurance pricing model that explicitly considers regulatory capital and bankruptcy costs. Based on the pricing deposit insurance model, we calculate the deposit insurance premiums of China's 16 listed banks with time span of 2011 to 2017 in this paper. The results demonstrate that the deposit insurance premiums of state-owned banks is lower than joint-stock commercial banks and city commercial banks, however, the deposit insurance premiums of joint-stock commercial banks is higher than city commercial banks. Numerical simulation shows that, ceteris paribus, the value of deposit insurance decreases with regulatory capital ratios and the insured deposits ratios, but it increases with interest rate and bankruptcy costs.     

An optimal investment strategy for a stream of liabilities generated by a step process in a financial market driven by a Lévy process

In this paper we investigate an asset–liability management problem for a stream of liabilities written on liquid traded assets and non-traded sources of risk. We assume that the financial market consists of a risk-free asset and a risky asset which follows a geometric Lévy process. The non-tradeable factor (insurance risk or default risk) is driven by a step process with a stochastic intensity. Our framework allows us to consider financial risk, systematic and unsystematic insurance loss risk (including longevity risk), together with possible dependencies between them. An optimal investment strategy is derived by solving a quadratic optimization problem with a terminal objective and a running cost penalizing deviations of the insurer’s wealth from a specified profit-solvency target. Techniques of backward stochastic differential equations and the weak property of predictable representation are applied to obtain the optimal asset allocation.     

标的资产价格服从跳-扩散过程的具有随机寿命的未定权益定价

本文在假设被终止或取消的风险与重大信息导致的标的资产价格跳跃的风险为非系统风险的情况下,应用无套利资本资产定价,推导出了标的的资产的价格服从跳-扩散过程具有随机寿命的未定权益满足的偏微分方程,然后应用Feynman-kac公式获得了未定权益的定价公式.