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Many discrete-time optimal stopping problems are known to have more tractable limit forms based on a planar Poisson process. Using this tool we find a solution to the optimal stopping problem for i.i.d. sequence of $n$ discrete uniform…
Structural results impose sufficient conditions on the model parameters of a Markov decision process (MDP) so that the optimal policy is an increasing function of the underlying state. The classical assumptions for MDP structural results…
In this paper we develop a deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples. As such, it is broadly applicable in situations where the underlying randomness can…
The problem of optimal stopping with finite horizon in discrete time is considered in view of maximizing the expected gain. The algorithm proposed in this paper is completely nonparametric in the sense that it uses observed data from the…
We consider portfolio optimization under a preference model in a single-period, complete market. This preference model includes Yaari's dual theory of choice and quantile maximization as special cases. We characterize when the optimal…
In this paper, we study the stochastic probing problem under a general monotone norm objective. Given a ground set $U = [n]$, each element $i \in U$ has an independent nonnegative random variable $X_i$ with known distribution. Probing an…
The turnpike phenomenon stipulates that the solution of an optimal control problem in large time, remains essentially close to a steady-state of the dynamics, itself being the optimal solution of an associated static optimal control…
In this paper we consider discrete and continuous time risk sensitive optimal stopping problem. Using suitable properties of the underlying Feller-Markov process we prove continuity of the optimal stopping value function and provide formula…
Selective labels are a common feature of consequential decision-making applications, referring to the lack of observed outcomes under one of the possible decisions. This paper reports work in progress on learning decision policies in the…
We develop methods to solve general optimal stopping problems with opportunities to stop that arrive randomly. Such problems occur naturally in applications with market frictions. Pivotal to our approach is that our methods operate on…
We investigate discrete-time mean-variance portfolio selection problems viewed as a Markov decision process. We transform the problems into a new model with deterministic transition function for which the Bellman optimality equation holds.…
A random sequence having two segments being the homogeneous Markov processes is registered. Each segment has his own transition probability law and the length of the segment is unknown and random. The transition probabilities of each…
We consider a vector of $N$ independent binary variables, each with a different probability of success. The distribution of the vector conditional on its sum is known as the conditional Bernoulli distribution. Assuming that $N$ goes to…
We study a decision-maker's problem of finding optimal monetary incentive schemes for retention when faced with agents whose participation decisions (stochastically) depend on the incentive they receive. Our focus is on policies constrained…
We investigate a class of optimal stopping problems arising in, for example, studies considering the timing of an irreversible investment when the underlying follows a skew Brownian motion. Our results indicate that the local directional…
We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed…
Heap monoids equipped with Bernoulli measures are a model of probabilistic asynchronous systems. We introduce in this framework the notion of asynchronous stopping time, which is analogous to the notion of stopping time for classical…
We investigate optimal stopping problems for systems driven by the Brownian sheet. Our analysis is divided into two parts. In the first part we derive explicit solutions to two optimal stopping problems for the exponentially discounted…
We study an infinite horizon optimal stopping problem which arises naturally in the optimal timing of a firm/project sale or in the valuation of natural resources: the functional to be maximised is a sum of a discounted running reward and a…
Suppose an online platform wants to compare a treatment and control policy, e.g., two different matching algorithms in a ridesharing system, or two different inventory management algorithms in an online retail site. Standard randomized…