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Fixed precision estimation of the maximal value of a bounded random variable

Andrzej Sierociński — 1986

Mathematica Applicanda

The object of this paper is to survey the methods of fixed precision estimation of the maximal value of a bounded random variable. In particular the paper gives solutions to this problem for a class of distributions with unknown scale parameter (section 2) and for a class of distributions with certain features of symmetry (section 3). The sequential procedures solving both subproblems are not only asymptotically consistent and asympto-tically efficient in the sense of Chow and Robbins (like that...

Optimal stopping of a risk process

Elżbieta FerensteinAndrzej Sierociński — 1997

Applicationes Mathematicae

Optimal stopping time problems for a risk process U t = u + c t - n = 0 N ( t ) X n where the number N(t) of losses up to time t is a general renewal process and the sequence of X i ’s represents successive losses are studied. N(t) and X i ’s are independent. Our goal is to maximize the expected return before the ruin time. The main results are closely related to those obtained by Boshuizen and Gouweleew [2].

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