一类奇异型折扣费用模型之推广

A CLASS OF EXTENDED SINGULAR MODELS OF DISCOUNTED PROBLEMS

设((?),(?),P)为一概率空间,(?)_t,t≥0为(?)中的上升(?)-域,W_t,t≥0为(?)_t,适应的标准 Wiener 过程,且对(?)0≤s≤t≤∞,W_t—W_s 与(?)_s 独立.以(?)表(?)_t 适应左连续0初值有限变差过程全体.对(?)ξ={ξ_t,t≥0}∈(?)有正规分解ξ_t=ξ_t^+—ξ_t^-,(?)_t(?)ξ_t^++ξ_t^-表ξ_t的全变差,当然ξ^+及ξ_-皆(?)中单调非降过程.有关类型的折扣费用问题曾被不少人研究过,例如 Bene(?)等人的文章.

In this paper,we construct a new class of singular models of disocounted problems,whichare an extension of the models in [2].For these extended models,we give conditions of theexistence of their optimal controls,and constructions of these optimal controls if they exist.