马氏链环境中复合二项风险模型(Compound binomial risk model in Markov-chain environment),简记 为MECM. Cossette(2004)对MECM的定义含混,文中以反例指出了这一点.严格地 建立了MECM($\text{It}\mathrm{\Theta }$, $\mathit{I}$, $\mathit{B}$),给出其特征四元组($\xi ,{\text{It}\mathrm{\Gamma }}_{\text{It}\mathrm{\Theta }},{\alpha }_I,F_B$). 该模型较Cossette(2004)广泛. 并且在给定一个四元组 ($\xi ,\text{It}\mathrm{\Gamma },\alpha ,F$)时, 证明了: 存在MECM($\text{It}\mathrm{\Theta }$, $\mathit{I}$,  $\mathit{B}$),其特征四元组与给定的($\xi ,\text{It}\mathrm{\Gamma },\alpha ,F$)重合.这里存在性证明是构造性的.

MECM is short for compound binomial risk model in Markov-chain environment. Definition and its conditions of MECM in Cossette(2004) are not clear enough, in this paper we point out it with a counterexample. The strictly MECM(, I , B) is established, and its characteristic 4-tuple (, ??, I , FB) is given. The new model in this paper is more extensive than the model in Cossette(2004). Moreover, one 4-tuple (, ??, , F) is given, it is shown that there exists MECM(, I , B), and its characteristic 4-tuple is just the above given (, ??, , F). The proof of the existence of the MECM(, I , B) is constructive.