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连续参数过程的最优停止

THE OPTIMAL STOPPING PROBLEM OF A CONTINUOUS PARAMETER PROCESS
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摘要 Suppose X = (Xr, Fr, t ∈ R+) be an optional reward process with ( Fr) satisfying usual conditions. In this paper, we correct the proof of existence about Snell envelope in [4] and the proof of an important lemma (Lemma 4. 6) in [5], and give a proof of existence about Snell envelope under certain conditions, i. e. EZx- 【 ∞ and Z is upper-semi-continuous on the right (USCR) or there is a stopping rule (SR)τ ≤σ such that EZx-∞ for any stopping rule σ . At the same time, we prove a four-repeated limit theorem when Z is continuous on the right. The character and the uniqueness of the optimal stopping time (OST) or optimal stopping rule (OSR) are discussed. Suppose X = (Xr, Fr, t ∈ R+) be an optional reward process with ( Fr) satisfying usual conditions. In this paper, we correct the proof of existence about Snell envelope in [4] and the proof of an important lemma (Lemma 4. 6) in [5], and give a proof of existence about Snell envelope under certain conditions, i. e. EZx- < ∞ and Z is upper-semi-continuous on the right (USCR) or there is a stopping rule (SR)τ ≤σ such that EZx-∞ for any stopping rule σ . At the same time, we prove a four-repeated limit theorem when Z is continuous on the right. The character and the uniqueness of the optimal stopping time (OST) or optimal stopping rule (OSR) are discussed.
作者 金治明
出处 《高校应用数学学报(A辑)》 CSCD 北大核心 1992年第1期 19-31,共13页 Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金 This paper is supported by pre-research fund of the University
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参考文献2

  • 1Xue Xinghong,数学研究与评论,1986年,6卷
  • 2Yen Jiaan,Introduction of martingale and stochastic integration,1982年

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