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A new characterization of excessive functions for arbitrary one–dimensional regular diffusion processes is provided, using the notion of concavity. It is shown that excessivity is equivalent to concavity in some suitable generalized sense. This permits a characterization of the value function of the optimal stopping problem as “the smallest nonnegative… (More)

- Peter I. Frazier, Warren B. Powell, Savas Dayanik
- INFORMS Journal on Computing
- 2009

We consider a Bayesian ranking and selection problem with independent normal rewards and a correlated multivariate normal belief on the mean values of these rewards. Because this formulation of the ranking and selection problem models dependence between alternatives’ mean values, algorithms may utilize this dependence to perform efficiently even when the… (More)

- Peter I. Frazier, Warren B. Powell, Savas Dayanik
- SIAM J. Control and Optimization
- 2008

In a sequential Bayesian ranking and selection problem with independent normal populations and common known variance, we study a previously introduced measurement policy which we refer to as the knowledge-gradient policy. This policy myopically maximizes the expected increment in the value of information in each time period, where the value is measured… (More)

- Savas Dayanik
- Math. Oper. Res.
- 2008

We propose a new solution method for optimal stopping problems with random discounting for linear diffusions whose state space has a combination of natural, absorbing, or reflecting boundaries. The method uses a concave characterization of excessive functions for linear diffusions killed at a rate determined by a Markov additive functional and reduces the… (More)

- Erhan Bayraktar, Savas Dayanik, Ioannis Karatzas
- ArXiv
- 2005

We study the quickest detection problem of a sudden change in the arrival rate of a Poisson process from a known value to an unknown and unobservable value at an unknown and unobservable disorder time. Our objective is to design an alarm time which is adapted to the history of the arrival process and detects the disorder time as soon as possible. In… (More)

A change in the arrival rate of a Poisson process sometimes necessitates immediate action. If the change time is unobservable, then the design of online change detection procedures becomes important and is known as the Poisson disorder problem. Formulated and partially solved by Davis [Banach Center Publ., 1 (1976) 65–72], the standard Poisson problem… (More)

- Savas Dayanik, Jing-Sheng Song, Susan H. Xu
- Manufacturing & Service Operations Management
- 2003

We consider an assemble-to-order (ATO) system: Components are made to stock by production facilities with finite capacities, and final products are assembled only in response to customers’ orders. The key performance measures in this system, such as order fill rates, involve evaluation of multivariate probability distributions, which is computationally… (More)

- René Carmona, Savas Dayanik
- Math. Oper. Res.
- 2008

Motivated by the analysis of financial instruments with multiple exercise rights of American type and mean reverting underlyers, we formulate and solve the optimal multiple-stopping problem for a general linear regular diffusion process and a general reward function. Instead of relying on specific properties of geometric Brownian motion and call and put… (More)

- Erhan Bayraktar, Savas Dayanik
- Math. Oper. Res.
- 2006

We solve the Poisson disorder problem when the delay is penalized exponentially. Our objective is to detect as quickly as possible the unobservable time of the change (or disorder) in the intensity of a Poisson process. The disorder time delimits two different regimes in which one employs distinct strategies (e.g., investment, advertising, manufacturing).… (More)

- Savas Dayanik, Angela J. Yu
- SIAM J. Control and Optimization
- 2013

Abstract. Any intelligent system performing evidence-based decision making under time pressure must negotiate a speed-accuracy trade-off. In computer science and engineering, this is typically modeled as minimizing a Bayes-risk functional that is a linear combination of expected decision delay and expected terminal decision loss. In neuroscience and… (More)