两指标随机过程的最优停止的构造

THE STRUCTURES OF OPTIMAL STOPPING FOR TWO INDEXES STOCHASTIC PROCESSES

本文研究了离散两指标随机过程X=(X_z,_z,z∈N^2)的最优停止的结构及X的Snell包络的渐近算法。首先证明了在条件(A^+)下:Γ=(γ_z,_z,z∈N^2)是控制X的最小正则上鞅,这里γ_z=E(X_σ|_z),z∈N^2。然后根据最优原理,利用X的Snell包络构造出最优策略。从而得出了报酬过程为X=(X_z,_z,z∈N^2)的最优停点的具体结构。最后证明了X的Snell包络的三重极限定理。

In this paper, it is researched that the structure of discrete two indexes stochastic processes X=(X_z, _z, z∈N^2) and the asymptotic arithmetic of Shell's envelope of X. At first, under the condition (A^+), it is proved that Γ=(γ_z,_z, z∈N^2) is minimal -regul alsupermatingale above X, where γ_z=E(X_σ|_z). Then optimal tactics is structured by Snell's envelope of X and optimal principle. Therfore, the structure of optimal stopping for payoff processes X= (X_z,, z∈N^2) are obtained. At last, three limit theorem for Snell's envelope of X is proved.