The main results : theorem 1 . 2 . 2 the function ( u ) - satisfies the integro - differential equation where , theorem 1 . 3 . 2 if * ( ) s analytic on the complex plane except for the roots of in second chapter , we consider a risk process in which inter - arrival times have a phase - type ( 2 ) distribution , a distribution with a density k ( t ) satisfying the following second order linear differential equation : the conditions are satisfied for all convolutions of two exponential distributions ( with not necessarily equal means ) 定理1 . 3 . 2若函数~ * ( )除了方程( 1 . 3 . 1 )的极点外，在整个复平面上都是解析的，则ddas 。 type风险模型是风险理论中应用比较广泛的一类风险模型dicksonandhipp （ 1998 ）研究了索赔时间间隔服从erlang间分布的情况，并于2001年aun了其罚金折现期望满k一积分微分方g
Credit consumption is that the consumers borrow from banks or other flnancial instit ' utions to buy goods or services for their persona1 use . its main form is consumer credit , that ' s also the main object to be researched in this paper . on the micro - economic aspect , consumer credit enables the consumers arrange their expenses neatly by using consumer credit , they can spend their fijture income to fulfi1l the demands of nowadays 信用消费方式的出现，使消费者在安排消费支出上更加灵活，能够预支未来收入，提前实现消费愿望，其经济意义从微观来看，有助于消费者克服流动性约束，进行跨时期消费选择，实现个人效用的最大化，从宏观来看，可以在居民收入预期稳定的条件下，有效地扩大现期消费需求，使产品价值能够顺利实现，推动社会再生产的循环发展。
In the first section of this chapter , we show that the expectation of the discounted penalty w ( u ) satisfies an integro - differential equation from which we derive the laplace transform of w ( u ) . the expectation of the distribution of the time to ruin ( t ) , the surplus prior to ruin ( s ( t - ) ) and the deficit at ruin ( s ( t ) ) 在本章中，罚金折现期望，破产概率，破产时的赤字，破产前的瞬间盈余的各阶距的渐近表达式，特别地，在n = 2时我们还得到了破产前的瞬间盈余，破产时的赤字以及它们联合分布的表达式。
