带干扰的多险种风险模型的破产概率

将多险种风险模型推广到带干扰项的一种新模型,讨论了收益过程的性质,并利用鞅的方法得出了破产概率所满足的Lundberg不等式及其一般公式.     

Vector-valued weak martingale Hardy spaces and atomic decompositions

Some atomic decomposition theorems are proved in vector-valued weak martingale Hardy spaces w _p Σ_α(X), w _p Q _α(X) and wD _α(X). As applications of atomic decompositions, a sufficient condition for sublinear operators defined on some vector-valued weak martingale Hardy spaces to be bounded is given. In particular, some weak versions of martingale inequalities for the operators f*, S ^(p)(f) and σ^(p)(f) are obtained. This research was supported by the National Science Foundation of China (No. 10371093).     

Quadratic Hedging Methods for Defaultable Claims

We apply the local risk-minimization approach to defaultable claims and we compare it with intensity-based evaluation formulas and the mean-variance hedging. We solve analytically the problem of finding respectively the hedging strategy and the associated portfolio for the three methods in the case of a default put option with random recovery at maturity.     

鞅的矩型极大算子的若干不等式

给出了算子T=∑_(n=1)~∞T_n在H_B~p和BMO_(p,B)~-上有界的一些充分条件,其中T_n(n∈P)为具有Δ性质的算子.作为应用,借助于算子值鞅变换得到了关于鞅的矩型极大算子的强(p,p)型不等式和弱(1,1)型不等式,以及其在BMO_(p,B)~-上的有界性.这些结果与经典H~p鞅论中极大算子的性质相对应.     

误差为鞅差序列的半参数回归模型估计的相合性

设半参数回归模型Ｙ（ｎ）ｉ＝β·ｘ（ｎ）ｉ＋ｇ（ｔ（ｎ）ｉ）＋Ｅ（ｎ）ｉ,ｉ＝１,２,…,ｎ,本文由最小二乘法和一般加权方法定义的β、ｇ（ｔ）的估计量βｎ,ｇｎ（ｔ）,在误差为鞅差序列下获得了βｎ,ｇｎ（ｔ）的ｒ（≥２）阶平均相合性．     

特殊半鞅的一个局部性质

本文讨论特殊半鞅的一个局部性质,将局部（平方可积）鞅的结果推广到了一类特殊半鞅的情形。     

Convergence of Appell Polynomials of Long Range Dependent Moving Averages in Martingale Differences

We study limit distribution of partial sums S_N,k(t) = _{s = 1} ^{[N t]} A_k(X_s) of Appell polynomials of the long-range dependent moving average process X_t> = _{i t} b_{t - i i}, where {_i} is a strictly stationary and weakly dependent martingale difference sequence, and b_i i^{d - 1} (0 < d < 1/2). We show that if k(1-2 d)<1, then suitably normalized partial sums S_N,k(t) converge in distribution to the kth order Hermite process. This result generalizes the corresponding results of Surgailis, and Avram and Taqqu obtained in the case of the i.i.d. sequence { _i}.     

具有混合保费收入的双险种二项风险模型

将双二项风险模型推广为具有混合保费收入的新模型,并运用鞅论的方法得出破产概率满足Lundberg不等式和一般表达式.     

基于鞅方法下分数布朗运动欧式回望期权的定价

利用分数布朗运动研究了一种强路径依赖型期权—回望期权的定价问题.首先列出了有关的定义和引理;其次利用该定义和引理建立了分数布朗运动情况下的价格模型,通过鞅方法,得到了回望期权价格所满足的方程;最后分别给出了看跌回望期权和看涨回望期权的定价公式的显式解.     

Convergence of branching transport processes to branching brownian motion

Two models are given of branching transport processes that converge to branching Brownian motion starting with one initial particle. The martingale problem method is used.