A version of the classical secretary problem is studied, in which one is interested in selecting one of the b best out of a group of n differently ranked persons who are presented one by one in a random order. It is assumed that b is bigger than or equal to 1 is a preassigned number. It is...

I introduce and evaluate a new stochastic simulation method for dynamic economic models. It is based on recent work in the operations research and engineering literatures (Van Roy et. al, 1997; Powell, 2007; Bertsekas, 2011). The baseline method involves rewriting the household's dynamic program in...

We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. The "curse of dimensionality" is avoided due to four complementary techniques: (1) exploiting...

In this paper, we state sufficiency, necessity, convergence, existence and uniqueness results for infinite horizon optimal control problems with unbounded payoffs in which the assumptions are very weak and there are no topological assumptions about the model components. We also state a sequence...

We discuss the precision with which financial models are handled, in particular optimisation models. We argue that precision is only required to a level that is justified by the overall accuracy of the model, and that this required precision should be specifically analysed, so to better...

Sequences of decisions that occur under uncertainty arise in a variety of settings, including transportation, communication networks, finance, defence, etc. The classic approach to find an optimal decision policy for a sequential decision problem is dynamic programming; however its usefulness is...

In this research, we study an optimal overhaul-replacement policy of a multi-degraded repairable system sold with a free replacement warranty. In the proposed replacement policy, a maintenance action and failure are dependent on a system degradation level and the system age, and hence the...

We introduce a novel semi-parametric estimator of the price of American options in a discrete time, Markovian framework. The estimator is based on a parametric specification of the stochasticdiscount factor and is non-parametric w.r.t. the historical dynamics of the state variables. The...

We formulate the maintenance scheduling decision as a dynamic optimization problem, subject to an accelerating decay. This approach offers a formal, yet intuitive, weighting of the trade-offs involved when deciding a maintenance schedule. The optimal maintenance schedule reflects the trade-off...