双指数跳扩散模型下远期生效期权的定价

用双指数跳扩散过程来刻画风险资产的价格,给出了远期生效期权的定价公式.将远期生效期期权的价格转化为两个数学期望的乘积,利用指数分布的性质和全期望公式给出远期生效期权的定价公式.     

双跳跃仿射扩散模型的几何平均型水平重置期权定价

在资产收益率及其波动率均满足随机跳跃且具有跳跃相关性的仿射扩散模型下,用广义双指数分布和伽玛分布分别刻画非对称性收益率及其波动率的跳跃波动变化,研究了具有几何平均特征的水平重置期权定价问题.通过Girsanov测度变换和多维Fourier逆变换方法,给出了此类重置期权定价的解析公式.最后,通过数值实例着重分析了联合跳跃...     

汽车保险中的BMS

ＢＭＳ在汽车保险中的应用是十分广泛的．本文讨论了如何在汽车保险中更有效地应用ＢＭＳ的方法,包括三部分：第一部分评介了基于索赔次数模型的最优ＢＭＳ;第二部分提出了公平ＢＭＳ的方法并讨论了其性质;第三部分分析了如何在ＢＭＳ中不仅考虑索赔次数而且考虑索赔额之大小,这里假设给定个体保单的索赔额服从参数为θ的指数分布,而保单组合关于θ的结构函数为伽玛分布．     

服从跳-扩散过程的几种资产的最大值的期权定价

本文利用了关于 Black- scholes方程的直观解释 ,以及采用了 Margrabe在推导交换期权定价公式时的手段 ,研究了 Merton跳 -扩散过程期权定价的一个特殊情况 ,并得到服从跳 -扩散过程的几种资产最大值的欧式看涨期权定价公式     

跳扩散模型下交换期权定价的Mellin变换方法

在资产价格服从跳扩散模型的条件下,利用Mellin变换的方法对交换期权定价.首先利用Feynman-Kac定理得到了交换期权的价格过程满足的偏积-微分方程.其次利用Mellin变换得到不依赖于跳跃大小分布的交换期权的定价公式.最后通过数值分析检验了此定价公式的准确性,并分析了期权价格与资产价格的关系.     

基于观察信息的分数B-S市场的欧式幂期权定价模型

本文讨论了基于观察信息的分数Black-Scholes市场中的幂期权定价问题,利用基于可观察的信息下的股票价格的条件分布公式,推导出欧式幂期权的定价公式,推广了有关的分数Black-Scholes市场中的期权定价的一些结果.     

基于GARCH模型考虑股本稀释作用的权证定价

考虑到认购权证对股本有稀释作用,把对认购权证定价转化为一个看涨期权的定价,运用GARCH模型得出看涨期权标的资产波动率的近似经验分布,根据期权定价的Black-Scholes公式,得出认购权证价格的近似分布.     

分形布朗运动下有交易成本的外汇期权定价

研究了有交易成本的分形Black-Scholes外汇期权定价问题.基于汇率的分形布朗运动分布假设,运用分形布朗运动的性质和随机微积分方法,得到了欧式外汇期权价格所满足的偏微分方程.最后,建立离散时间条件下的非线性期权定价模型,并且通过解期权价格的偏微分方程给出了有交易成本的欧式外汇期权定价公式.     

双跳跃仿射扩散模型的美式看跌期权定价北大核心CSCD

美式期权是一类具有提前实施权利的奇异型合约.2000年Duffie等人提出了一类双跳跃仿射扩散模型,假定标的资产及其波动率过程具有相关的共同跳跃,且波动率过程的跳跃大小服从指数分布.文章扩展了该模型,允许波动率过程的跳跃大小服从伽玛分布,并在具有跳跃风险的随机利率环境下研究美式看跌期权的定价.应用Bermudan期权和Richardson插值加速方法给出了美式看跌期权价格计算的解析近似公式.用数值计算实例,以最小二乘蒙特卡罗模拟法检验文章结果的准确性和有效性.最后,分析了常利率与随机利率情形下波动率过程中的相关系数对期权价格的影响.结果表明,相关系数对美式期权价格的作用是反向的.文章结果可以应用于利率与信用衍生品的定价研究.     

混合分数布朗运动环境下欧式障碍期权定价

当股票价格遵循混合分数布朗运动时,利用Δ-对冲和混合分数It8公式,建立混合分数布朗运动下欧式障碍期权定价模型,通过换元法将期权定价的偏微分方程转化为热传导方程,求得显示解.在此基础上,得到欧式障碍期权看涨-看跌平价关系式.由此,再根据敲入-敲出障碍期权关系式可推出障碍期权所有类型的定价公式.     

Securitization of motor insurance loss rate risks

In an attempt to transfer the loss rate risks in motor insurance to the capital market, we use the tranche technique to hedge the motor insurance risks. This paper illustrates AXA and their securitization of French motor insurance in 2005 as an example. Though this application is new, this transaction is based on a concept similar to CDOs. Tranches of bonds are constructed on the basis of the expected loss ratio from motor insurance policy holders’ groups. As a consequence we develop motor loss rate bonds using the structure of synthetic CDOs. The coupon payments of each tranche depend on the level of the loss rates of the underlying motor insurance pool. We show the integral formulas for the loss tranche contract where the loss distribution is modelled with discounted compound Poisson process. Esscher transform is chosen for a risk adjusted measure change and Fourier inversion method is used to calculate the price of the motor claim rate securities. The pricing methods of the tranches are illustrated, and possible suggestions to improve the pricing method and the design of these new securities follow.     

Severity modeling of extreme insurance claims for tariffication

Generalized linear models are common instruments for the pricing of non-life insurance contracts. They are used to estimate the expected frequency and severity of insurance claims. However, these models do not work adequately for extreme claim sizes. To accommodate for these extreme claim sizes, we develop the threshold severity model, that splits the claim size distribution in areas below and above a given threshold. More specifically, the extreme insurance claims above the threshold are modeled in the sense of the peaks-over-threshold methodology from extreme value theory using the generalized Pareto distribution for the excess distribution, and the claims below the threshold are captured by a generalized linear model based on the truncated gamma distribution. Subsequently, we develop the corresponding concrete log-likelihood functions above and below the threshold. Moreover, in the presence of simulated extreme claim sizes following a log-normal as well as Burr Type XII distribution, we demonstrate the superiority of the threshold severity model compared to the commonly used generalized linear model based on the gamma distribution.     

Stochastic comparison of aggregate claim amounts between two heterogeneous portfolios and its applications

The aggregate claim amount in a particular time period is a quantity of fundamental importance for proper management of an insurance company and also for pricing of insurance coverages. In this paper, we show that the proportional hazard rates (PHR) model, which includes some well-known distributions such as exponential, Weibull and Pareto distributions, can be used as the aggregate claim amount distribution. We also present some conditions for the use of exponentiated Weibull distribution as the claim amount distribution. The results established here complete and extend the well-known result of Khaledi and Ahmadi (2008).     

Jump diffusion processes and their applications in insurance and finance

For insurance risks, jump processes such as homogeneous/non-homogeneous compound Poisson processes and compound Cox processes have been used to model aggregate losses. If we consider the economic assumption of a positive interest to aggregate losses, Lévy processes have proven to be useful. Also in financial modelling, it has been observed that diffusion models are not robust enough to capture the appearance of jumps in underlying asset prices and interest rates. As a result, jump diffusion processes, which are, simply speaking, combinations of compound Poisson processes with Brownian motion, have gained popularity for modelling in insurance and finance. In this paper, considering a jump diffusion process, we obtain the explicit expression of the joint Laplace transform of the distribution of a jump diffusion process and its integrated process, assuming that jump size follows the mixture of two exponential distributions, which is a special case of phase-type distributions. Based on this Laplace transform, we derive the moments of the aggregate accumulated claim amounts of insurance risk. For a financial application, we concern non-defaultable zero-coupon bond pricing. We also provide several numerical examples for the moments of aggregate accumulated claims and default-free zero-coupon bond prices.     

Pricing general insurance in a reactive and competitive market

A simple parameterisation is introduced which represents the insurance market’s response to an insurer adopting a pricing strategy determined via optimal control theory. Claims are modelled using a lognormally distributed mean claim size rate, and the market average premium is determined via the expected value principle. If the insurer maximises its expected wealth then the resulting Bellman equation has a moving boundary in state space that determines when it is optimal to stop selling insurance. This stochastic optimisation problem is simplified by the introduction of a stopping time that prevents an insurer leaving and then re-entering the insurance market. Three finite difference schemes are used to verify the existence of a solution to the resulting Bellman equation when there is market reaction. All of the schemes use a front-fixing transformation. If the market reacts, then it is found that the optimal strategy is altered, in that premiums are raised if the strategy is of loss-leading type and lowered if it is optimal for the insurer to set a relatively high premium and sell little insurance.     

Pricing general insurance in a reactive and competitive market

A simple parameterisation is introduced which represents the insurance market’s response to an insurer adopting a pricing strategy determined via optimal control theory. Claims are modelled using a lognormally distributed mean claim size rate, and the market average premium is determined via the expected value principle. If the insurer maximises its expected wealth then the resulting Bellman equation has a moving boundary in state space that determines when it is optimal to stop selling insurance. This stochastic optimisation problem is simplified by the introduction of a stopping time that prevents an insurer leaving and then re-entering the insurance market. Three finite difference schemes are used to verify the existence of a solution to the resulting Bellman equation when there is market reaction. All of the schemes use a front-fixing transformation. If the market reacts, then it is found that the optimal strategy is altered, in that premiums are raised if the strategy is of loss-leading type and lowered if it is optimal for the insurer to set a relatively high premium and sell little insurance.     

Bayesian multivariate Poisson models for insurance ratemaking

When actuaries face the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or a homeowner’s insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce different multivariate Poisson regression models in order to relax the independence assumption, including zero-inflated models to account for excess of zeros and overdispersion. These models have been largely ignored to date, mainly because of their computational difficulties. Bayesian inference based on MCMC helps to resolve this problem (and also allows us to derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claim. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models together with their zero-inflated versions.     

双险种最优再保险策略

本文对双险种风险模型,在一险种采取比例再保险,另一险种采取超出损失再保险策略下,得到调节系数与再保险自留水平之间的函数关系式,在理赔额为指数分布和Erlang(2)分布的条件下,得到最优比例再保险和超出损失再保险的自留水平,以及调节系数最大值。     

Exponential functionals of Lévy processes and variable annuity guaranteed benefits

Exponential functionals of Brownian motion have been extensively studied in financial and insurance mathematics due to their broad applications, for example, in the pricing of Asian options. The Black–Scholes model is appealing because of mathematical tractability, yet empirical evidence shows that geometric Brownian motion does not adequately capture features of market equity returns. One popular alternative for modeling equity returns consists in replacing the geometric Brownian motion by an exponential of a Lévy process. In this paper we use this latter model to study variable annuity guaranteed benefits and to compute explicitly the distribution of certain exponential functionals.     

Research on Ruin Probability of Risk Model Based on AR(1) Time Series

The insurance industry typically exploits ruin theory on collected data to gain more profits. However, state-of-art approaches fail to consider the dependency of the intensity of claim numbers, resulting in the loss of accuracy. In this work, we establish a new risk model based on traditional AR(1) time series, and propose a fine-gained insurance model which has a dependent data structure. We leverage Newton iteration method to figure out the adjustment coefficient and evaluate the exponential upper bound of the ruin probability. We claim that our model significantly improves the precision of insurance model and explores an interesting direction for future research.