GAME THEORETIC ANALYSIS FOR AN OPTIMAL STOPPING PROBLEM BY MEANS OF MOMENTS OF A DISTRIBUTION FUNCTION

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Let X_1,X_2,…, X_n,…be mutually independent random variables with a common cdf F, which is unknown but belongs to some class F of cdf's. The class F = F(μ,σ^2,M) is the set of all cdf's whose mean, variance and domain are -∞ < μ < ∞,0 < σ^2 < ∞, and [μ - M, μ + M] respectively. It is assumed that they are known. Under an observation cost c,0 < c < ∞, we consider a stopping problem φ(x, F) as a two-person zero-sum game in which the. player I decides his stopping set {X > x}, x ∈ R, and the player 2 chooses her cdf F in F. We analyze the upper bound problem φ^δ = sup_<x∈R>sup_<F∈F>φ(x, F) and the game problem φ^δ = value_<x∈R>_<F∈F>φ(x, F) to derive a simple and meaningful solution with the parameters c,μ,σ and M.
社団法人日本オペレーションズ・リサーチ学会の論文