限制市场中不定权益的定价

通过构造一族辅助风险溢价来确定不定权益的无套利价格，用这种方法 讨论了存在交易限制时欧式不定权益的定价问题，其结果与Davis的公平价格一致.     

Explosive Random‐Coefficient AR(1) Processes and Related Asymptotics for Least‐Squares Estimation

Abstract. Large sample properties of the least‐squares and weighted least‐squares estimates of the autoregressive parameter of the explosive random‐coefficient AR(1) process are discussed. It is shown that, contrary to the standard AR(1) case, the least‐squares estimator is inconsistent whereas the weighted least‐squares estimator is consistent and asymptotically normal even when the error process is not necessarily Gaussian. Conditional asymptotics on the event that a certain limiting random variable is non‐zero is also discussed.     

随机指标鞅序列的收敛性

主要讨论了以停时序列{τn}n∈N作为鞅序列{xn}n∈N的指标时,序列{xτn}n∈N的收敛性问题.     

线性红利下带干扰的复合Poisson风险模型

在线性红利下将保单到达过程推广为Poisson过程,并通过添加Brownian运动来刻画保险公司不确定的收益和付款,建立线性红利下带干扰的复合Poisson风险模型.运用鞅方法得出了破产概率满足的Lundberg不等式和一般公式,并给出了生存概率满足的积分—微分方程。     

带干扰的变破产下限多险种风险模型

近年来许多文献在研究风险模型的破产概率时假设破产下限为0,而在实际保险实务中,当保险公司的盈余过程低于某一限度时,保险公司就面临着破产,针对该问题,讨论了带干扰的多险种风险模型下的破产概率,运用鞅方法推导出破产概率满足的不等式和具体的表达式,给出了推广后的多险种风险模型中变破产下限破产概率所满足的不等式和具体表达式。     

基于跳跃-扩散过程的亚式期权定价

在标的资产价格跳过程为更新过程的假设下,研究了具有浮动敲定价格的亚式期权,通过自融资交易复制将路径依赖的亚式期权定价问题转化为与路径无关的微分方程的求解问题,拓展了刘宣会的结果。     

在分数Brown运动环境下具有红利支付期权定价的鞅分析

本文在分数Brown运动环境下,利用基础资产价格逼近过程的鞅性,推导分析了具有红利支付时期期权定价方程.     

Performance analysis of stochastic gradient algorithms under weak conditions

By using the stochastic martingale theory, convergence properties of stochastic gradient （SG） identification algorithms are studied under weak conditions. The analysis indicates that the parameter estimates by the SG algorithms consistently converge to the true parameters, as long as the information vector is persistently exciting （i.e., the data product moment matrix has a bounded condition number） and that the process noises are zero mean and uncorrelated. These results remove the strict assumptions, made in existing references, that the noise variances and high-order moments exist, and the processes are stationary and ergodic and the strong persis- tent excitation condition holds. This contribution greatly relaxes the convergence conditions of stochastic gradient algorithms. The simulation results with bounded and unbounded noise variances confirm the convergence conclusions proposed.     

一类推广的基于进入过程的多险种风险模型

对索赔到达过程为Poisson过程的单险种风险模型进行推广,讨论了带干扰的基于进入过程且索赔到达过程是复合Poisson-Geometric过程的多险种风险模型,并应用鞅方法得到了该模型满足的Lundberg不等式和破产概率的表达式.     

综合Cox风险模型的破产概率

针对实际情况,在保单到达过程和理赔过程均为Cox过程的基础上,引入了随机利率、投资收益、退保因素,并且要求退保过程的累计强度过程仍为Cox过程,从而得到一个综合的Cox风险模型,并利用鞅论的有关知识对该模型进行研究,进而得到该综合的Cox风险模型的最终破产概率的Lundberg不等式上界表达式.