F. Thomas Bruss

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The full-information secretary problem in which the objective is to minimize the expected rank is seen to have a value smaller than 7/3 for all n (the number of options). This can be achieved by a simple memoryless threshold rule. The asymptotically optimal value for the class of such rules is about 2.3266. For a large finite number of options, the optimal(More)
We consider a generalization of the house-selling problem to selling k houses. Let the offers, X 1 , X 2 ,. . ., be independent, identically distributed k-dimensional random vectors having a known distribution with finite second moments. The decision maker is to choose simultaneously k stopping rules, N 1 ,. .. , N k , one for each component. The payoff is(More)
We consider auctions in which the winning bid is the smallest bid that is unique. Only the upper-price limit is given. Neither the number of participants nor the distribution of the offers are known, so that the problem of placing a bid to win with maximum probability looks, a priori, ill-posed. Indeed, the essence of the problem is to inject a (final)(More)
How should we invest capital into a sequence of investment opportunities , if, for reasons of external competition, our interest focuses on trying to invest in the very best opportunity? We introduce new models to answer such questions. Our objective is to formulate them in a way that makes results high-risk specific in order to present true alternatives to(More)
known continuous distribution function. Robbins' problem is to find a sequential stopping rule without recall which minimizes the expected rank of the selected observation. An upper bound (obtained by memoryless threshold rules) and a procedure to obtain lower bounds of the value are known, but the essence of the problem is still unsolved. The difficulty is(More)
Consider N balls that are distributed among V urns according to some distribution G. We do not see the outcome and now have to place one ball into one urn with the goal of maximizing the probability that it will be the left-most urn containing a single ball. How should we proceed? This is the urn-model translation of an interesting problem posed by an(More)
This talk presents an attempt to unify sequential search and selection problems in the light of optimal stopping problems on strings. The basic model is as follows: Strings are generated by sequences of letters or other codes produced by independent draws from a given alphabet or another source. The law of drawing different letters or expressions may be(More)
How should we invest capital into a sequence of investment opportunities , if, for reasons of external competition, our interest focuses on trying to invest in the very best opportunity? We introduce new models to answer this question by assuming that an investment on the very best yields a lucrative , possibly time-dependent, rate of return, that(More)
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