资产跳跃下CM策略多期收入保证价格模拟——基于条件蒙特卡罗方法

恒定混合策略(CM策略)多期收入保证价格是保本基金发行方采取设置止损的CM策略作为投资策略时收取保本费的理论依据,其中标的资产由复合泊松过程和维纳过程共同驱动,这一定价问题内嵌奇异期权,蒙特卡罗模拟方法擅长处理这种高维数量金融问题.基于风险中性测度推导出多期收入保证价格的现值表达式,用条件蒙特卡罗推导出这一现值表达式的模拟公式.在给定参数下分别用普通蒙特卡罗和条件蒙特卡罗计算CM策略多期收入保证价格的数值解,结果显示两种蒙特卡罗方法均能有效计算其数值解,之后通过给定显著性水平下的置信区间长度评价两种方法的精确度,结果显示条件蒙特卡罗比普通蒙特卡罗有很大改进.接着运用条件蒙特卡罗模拟研究多期收入保证价格对不同参数范围的变化情况.     

完全数据下Weibull分布参数的极大似然估计

在完全数据条件下对Weibull分布,分别使用Newton-Raphson算法、CM算法及修正的CM算法进行完全数据Weibull分布参数的极大似然估计计算,并且在得到相应的迭代公式后,进行随机模拟.从模拟结果来分析这三种算法在处理Weibull分布参数的极大似然估计的优良性.     

非负费用折扣半马氏决策过程

本文考虑可数状态非负费用的折扣半马氏决策过程.首先在给定半马氏决策核和策略下构造一个连续时间半马氏决策过程,然后用最小非负解方法证明值函数满足最优方程和存在ε-最优平稳策略,并进一步给出最优策略的存在性条件及其一些性质.最后,给出了值迭代算法和一个数值算例.     

蒙特卡罗方法计算定积分的进一步讨论

介绍了蒙特卡罗方法计算定积分的原理和方法.给出了用蒙特卡罗方法计算定积分的一个简单证明,从而揭示了蒙特卡罗方法和定积分定义间的内在联系.针对蒙特卡罗方法收敛慢的特点,提出将蒙特卡罗方法与相应的数值计算方法相结合,提高计算结果的精度.此外,将蒙特卡罗方法推广到反常积分上去.     

具有随机保费和交易费用的最优投资-再保险策略

本文研究具有随机保费和交易费用的最优投资和再保险策略选择问题.保险公司的盈余通过跳-扩散过程来模拟,假设保费收入是随机的.我们的研究目标是寻找一个最优再保险和投资策略,最大化投资终止时刻财富的期望效用.应用随机控制理论,我们得到最优投资-再保险策略和值函数的显式解.通过数值计算,我们给出模型参数对最优策略的影响.结果揭示了一些令人感兴趣的现象,它们可以对实际中的再保险和投资予以指导.     

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.     

数值问题的算法及其误差

数值问题是指这样一类数学问题 ,它从一组已知数据出发 ,求得一组结果数据 ,这两组数据问题要满足事先确定的一种关系 .也就是说数值问题强调数值结果 ,比如 ,讨论二元一次方程组　　 a11x1+a12 x2 =b1a2 1x1+a2 2 x2 =b2解的存在性和唯一性是一个数学问题 ,而当系数a11,a12 ,a2 1,a2 2 和右端项b1,b2 给定时要求出解x1,x2 的具体值这就是数值问题 .数值问题的求解方法被称为数值计算方法 ,电子计算机发展到今天 ,已成为大型数值计算的主要工具 ,因此必须研究适合于计算机使用的数值计算方法 .具体来说 ,用计算机解决数值问题要经历如下过程…     

广义带导数的非线性Schrdinger方程的动态分析和精确解

利用动力系统方法,针对广义带导数的非线性Schrdinger方程的精确解问题进行研究分析.采用行波变换,将其化为常微分方程动力系统;计算出该方程动力系统的首次积分,讨论了系统在不同参数条件下的奇点与相图,得到对应的精确解,包括孤立波解、周期波解、扭结波解和反扭结波解.运用数值模拟的方法,对方程的光滑孤立波解和周期波解等进行了数值模拟.分析计算获得的结果完善了相关文献已有的研究成果.     

最小化破产概率的保险人鲁棒投资再保险策略研究

在模型不确定条件下,研究以破产概率最小化为目标的模糊厌恶型保险公司的最优投资再保险问题. 假设保险公司可投资于一种风险资产,也可购买比例再保险. 分别考虑风险资产的价格过程服从随机波动率模型和非随机波动率模型的两种情况,根据动态规划原理建立相应的HJB方程,得到保险公司的最优鲁棒投资再保险策略和价值函数的解析解. 最后,通过数值模拟分析了各模型参数对最优策略和价值函数的影响.     

跳扩散市场投资组合研究

研究了连续时间动态均值-方差投资组合选择问题.假设风险资产价格服从跳跃-扩散过程且具有卖空约束.投资者的目标是在给定期望终止时刻财富条件下,最小化终止时刻财富的方差.通过求解模型相应的Hamilton-Jacobi-Bellmen方程,得到了最优投资策略及有效前沿的显示解.结果显示,风险资产的卖空约束及价格过程的跳跃因素对最优投资策略及有效前沿的是不可忽略的.     

Rare Events in Random Geometric Graphs

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions for a variety of conditional probabilities related to the number of edges in the random geometric graph and develop conditional Monte Carlo algorithms for estimating rare-event probabilities on this basis. We prove rigorously a reduction in variance when compared to the crude Monte Carlo estimators and illustrate the magnitude of the improvements in a simulation study. In higher dimensions, we use conditional Monte Carlo to remove the fluctuations in the estimator coming from the randomness in the Poisson number of nodes. Finally, building on conceptual insights from large-deviations theory, we illustrate that importance sampling using a Gibbsian point process can further substantially reduce the estimation variance.

     

Exact inference for a simple step-stress model from the exponential distribution under time constraint

In reliability and life-testing experiments, the researcher is often interested in the effects of extreme or varying stress factors such as temperature, voltage and load on the lifetimes of experimental units. Step-stress test, which is a special class of accelerated life-tests, allows the experimenter to increase the stress levels at fixed times during the experiment in order to obtain information on the parameters of the life distributions more quickly than under normal operating conditions. In this paper, we consider the simple step-stress model from the exponential distribution when there is time constraint on the duration of the experiment. We derive the maximum likelihood estimators (MLEs) of the parameters assuming a cumulative exposure model with lifetimes being exponentially distributed. The exact distributions of the MLEs of parameters are obtained through the use of conditional moment generating functions. We also derive confidence intervals for the parameters using these exact distributions, asymptotic distributions of the MLEs and the parametric bootstrap methods, and assess their performance through a Monte Carlo simulation study. Finally, we present two examples to illustrate all the methods of inference discussed here.     

Basket options valuation for a local volatility jump-diffusion model with the asymptotic expansion method

In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expansion method to approximate the conditional expectation of the stochastic variance associated with the basket value process. The numerical tests show that the suggested method is fast and accurate in comparison with the Monte Carlo and other methods in most cases.     

Basket options valuation for a local volatility jump–diffusion model with the asymptotic expansion method

In this paper we discuss the basket options valuation for a jump–diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expansion method to approximate the conditional expectation of the stochastic variance associated with the basket value process. The numerical tests show that the suggested method is fast and accurate in comparison with the Monte Carlo and other methods in most cases.     

Asymptotic representations for importance-sampling estimators of value-at-risk and conditional value-at-risk

Value-at-risk (VaR) and conditional value-at-risk (CVaR) are important risk measures. They are often estimated by using importance-sampling (IS) techniques. In this paper, we derive the asymptotic representations for IS estimators of VaR and CVaR. Based on these representations, we are able to prove the consistency and asymptotic normality of the estimators and to provide simple conditions under which the IS estimators have smaller asymptotic variances than the ordinary Monte Carlo estimators.     

Valuation of the interest rate guarantee embedded in defined contribution pension plans

In this research, we derive the valuation formulae for a defined contribution pension plan associated with the minimum rate of return guarantees. Different from the previous studies, we work on the rate of return guarantee which is linked to the δ-year spot rate. The payoffs of interest rate guarantees can be viewed as a function of the exchange option. By employing Margrabe’s [Margrabe, W., 1978. The value of an option to exchange one asset for another. Journal of Finance 33, 177–186] option pricing approach, we derive general pricing formulae under the assumptions that the interest rate dynamics follow a single-factor HJM (1992) [Heath. D. et al., 1992. Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation. Econometrica 60, 77–105] interest rate model and the asset prices follow a geometric Brownian motion. The volatility of the forward rates is assumed to be exponentially decaying. The formula is explicit for valuing maturity guarantee (type-I guarantee). For multi-period guarantee (type-II guarantee), the analytical formula only exists when the guaranteed rate is the one-year spot rate. The accuracy of the valuation formulae is illustrated with numerical analysis. We also investigate the effect of mortality and the sensitivity of key parameters on the value of the guarantee. We find that type-II guarantee is much more costly than the type-I guarantee, especially with a long duration policy. The closed form solution provides the advantage in valuing pension guarantees.     

Some closed form robust moment‐based estimators for the MEM(1,1)

In this paper, we extend the closed form moment estimator (ordinary MCFE) for the autoregressive conditional duration model given by Lu et al (2016) and propose some closed form robust moment‐based estimators for the multiplicative error model to deal with the additive and innovational outliers. The robustification of the closed form estimator is done by replacing the sample mean and sample autocorrelation with some robust estimators. These estimators are more robust than the quasi‐maximum likelihood estimator (QMLE) often used to estimate this model, and they are easy to implement and do not require the use of any numerical optimization procedure and the choice of initial value. The performance of our proposal in estimating the parameters and forecasting conditional mean μ_t of the MEM(1,1) process is compared with the proposals existing in the literature via Monte Carlo experiments, and the results of these experiments show that our proposal outperforms the ordinary MCFE, QMLE, and least absolute deviation estimator in the presence of outliers in general. Finally, we fit the price durations of IBM stock with the robust closed form estimators and the benchmarks and analyze their performances in estimating model parameters and forecasting the irregularly spaced intraday Value at Risk.     

Maximum likelihood estimation of multinomial probit factor analysis models for multivariate t-distribution

We propose a model for multinomial probit factor analysis by assuming t-distribution error in probit factor analysis. To obtain maximum likelihood estimation, we use the Monte Carlo expectation maximization algorithm with its M-step greatly simplified under conditional maximization and its E-step made feasible by Monte Carlo simulation. Standard errors are calculated by using Louis’s method. The methodology is illustrated with numerical simulations.     

基于信用风险修正的多阶段银行资产组合优化模型

从资产组合管理角度出发,用信用风险修正的方法对企业信用等级阈值进行修正,同时考虑商业银行持续经营的特点,将修正后的信用风险引入到多阶段的模型当中去,建立一个基于信用风险修正的多阶段银行资产组合优化模型.针对该模型的特点,给出了把Monte Carlo模拟的动态算法和改进粒子群的多阶段算法相结合求解方法.数值试验表明所建...     

Hybrid schemes for exact conditional inference in discrete exponential families

Exact conditional goodness-of-fit tests for discrete exponential family models can be conducted via Monte Carlo estimation of p values by sampling from the conditional distribution of multiway contingency tables. The two most popular methods for such sampling are Markov chain Monte Carlo (MCMC) and sequential importance sampling (SIS). In this work we consider various ways to hybridize the two schemes and propose one standout strategy as a good general purpose method for conducting inference. The proposed method runs many parallel chains initialized at SIS samples across the fiber. When a Markov basis is unavailable, the proposed scheme uses a lattice basis with intermittent SIS proposals to guarantee irreducibility and asymptotic unbiasedness. The scheme alleviates many of the challenges faced by the MCMC and SIS schemes individually while largely retaining their strengths. It also provides diagnostics that guide and lend credibility to the procedure. Simulations demonstrate the viability of the approach.