Yaakov Malinovsky

We consider a finite horizon optimal stopping problem for a sequence of independent and identically distributed random variables, where the objective is to design stopping rules that attempt to select the random variable with the highest value in the sequence. The performance of any stopping rule may be benchmarked relative to the selection of a ‘prophet’ that has perfect foreknowledge of the largest value. Such comparisons are typically stated in the form of ‘prophet inequalities’. We develop a game-theoretic characterization that supports a principled approach for deriving sharp non-asymptotic prophet inequalities for single-threshold stopping rules. We demonstrate that sharp constants in the ratio- and difference-type prophet inequalities are determined by the optimal values of an infinite two-person zero-sum game on the unit square with particular payoff kernels, while the solutions to the game provide optimal stopping rules and least favorable distributions. Among other things, this formulation also allows a systematic way to tackle restricted classes of distributions. The proposed framework leads to a numerically efficient algorithmic paradigm that allows the computing of sharp constants in prophet inequalities with any prescribed level of accuracy.

The 9th International Workshop in Sequential Methodologies, or IWSM-2026 (website: https://www.american.edu/cas/iwsm2026/) was held at American University in Washington, DC, on June 1–4, 2026. The ...

We consider a general class of round-robin tournament models of equally strong players. In these models, each of the n players competes against every other player exactly once. For each match between two players, the outcome is a value from a countable subset of the unit interval, and the scores of the two players in a match sum to one. The final score of each player is defined as the sum of the scores obtained in matches against all other players. We study the distribution of extreme scores, including the maximum, second maximum, and lower-order extremes. Since the exact distribution is computationally intractable even for small values of n , we derive asymptotic results as the number of players n tends to infinity, including limiting distributions, and rates of convergence.

We revisit a version of the classic occupancy scheme, where balls are thrown until almost all boxes receive a given number of balls. Special cases are widely known as coupon-collectors and dixie cup problems. We show that as the number of boxes tends to infinity, the distribution of the maximal occupancy count does not converge, but can be approximated by a convolution of two Gumbel distributions, with the approximating distribution having oscillations close to periodic on a logarithmic scale. We pursue two approaches: one relies on lattice point processes obtained by poissonisation of the number of balls and boxes, and the other employs interpolation of the multiset of occupancy counts to a point process on reals. This way we gain considerable insight in known asymptotics obtained previously by mostly analytic tools. Further results concern the moments of maximal occupancy counts and ties for the maximum.

We revisit a version of the classic occupancy scheme, where balls are thrown until almost all boxes receive a given number of balls. Special cases are widely known as coupon-collectors and dixie cup problems. We show that as the number of boxes tends to infinity, the distribution of the maximal occupancy count does not converge, but can be approximated by a convolution of two Gumbel distributions, with the approximating distribution having oscillations close to periodic on a logarithmic scale. We pursue two approaches: one relies on lattice point processes obtained by poissonisation of the number of balls and boxes, and the other employs interpolation of the multiset of occupancy counts to a point process on reals. This way we gain considerable insight in known asymptotics obtained previously by mostly analytic tools. Further results concern the moments of maximal occupancy counts and ties for the maximum.