L.A. Shepp has posed aild analyzed the problem of optimal random drawinp with Jut replacement from an urn containing predetermined numbers of plus and minus balls. ;Here Shepp’s results are extended by improving the bounds on value; of penturbeu urns, deriving an exact algorithm for the urn values and computing the stopping boundary for urns of u-, tn 200 balls.

Consider a graph G and a random walk on it. We want to stop the random walk at certain times (using an optimal stopping rule) to obtain independent samples from a given distribution ρ on the nodes. For an undirected graph, the expected time between consecutive samples is maximized by a distribution equally divided between two nodes, and so the worst expected time is 1/4 of the maximum commute t...

A method is proposed to solve optimal stopping problems. Several examples classical and new ones are discussed. Especially the values of American options (straddle and strangle) with infinite horizon are calculated.

Investment is often irreversible: once installed, capital has little or no value unless used in production. This paper proposes, solves and characterizes a model of sequential irreversible investment by a firm facing uncertainty in technology, demand and price of capital. The solution can be found in closed form if simple (but not totally unrealistic) functional forms are assumed, and can be gi...

In many decentralized labor markets, job candidates are offered positions at very early stages in the hiring process. It has been argued that these early offers are an effect of the competition between employers for the best candidate. This work studies the timing of offers in a theoretical model based on the classical secretary problem. We consider a secretary problem with multiple employers a...

We consider the stochastic-game-analogue of McKean’s optimal stopping problem when the underlying source of randomness is a spectrally negative Lévy process. Compared to the solution for linear Brownian motion given in Kyprianou (2004) one finds two new phenomena. Firstly the breakdown of smooth fit and secondly the stopping domain for one of the players ‘thickens’ from a singleton to an interv...