Optimal Stopping Times for Estimating Bernoulli Parameters with Applications to Active Imaging

2018 ◽  
Author(s):  
Safa C. Medin ◽  
John Murray-Bruce ◽  
Vivek K Goyal
Keyword(s):  
Optimal Stopping ◽  
Stopping Times ◽  
Active Imaging ◽  
Optimal Stopping Times

Optimal stopping with discount and observation costs

2000 ◽  
Vol 37 (01) ◽  
pp. 64-72 ◽  
Author(s):  
Robert Kühne ◽  
Ludger Rüschendorf
Keyword(s):  
Differential Equations ◽  
Optimal Stopping ◽  
Point Processes ◽  
Numerical Solutions ◽  
Domain Of Attraction ◽  
Approximate Solutions ◽  
Poisson Approximation ◽  
Stopping Times ◽  
Optimal Stopping Problem ◽  
Optimal Stopping Times

For i.i.d. random variables in the domain of attraction of a max-stable distribution with discount and observation costs we determine asymptotic approximations of the optimal stopping values and asymptotically optimal stopping times. The results are based on Poisson approximation of related embedded planar point processes. The optimal stopping problem for the limiting Poisson point processes can be reduced to differential equations for the boundaries. In several cases we obtain numerical solutions of the differential equations. In some cases the analysis allows us to obtain explicit optimal stopping values. This approach thus leads to approximate solutions of the optimal stopping problem of discrete time sequences.

Optimal stopping with discount and observation costs

2000 ◽  
Vol 37 (1) ◽  
pp. 64-72 ◽  
Author(s):  
Robert Kühne ◽  
Ludger Rüschendorf
Keyword(s):  
Differential Equations ◽  
Optimal Stopping ◽  
Point Processes ◽  
Numerical Solutions ◽  
Domain Of Attraction ◽  
Approximate Solutions ◽  
Poisson Approximation ◽  
Stopping Times ◽  
Optimal Stopping Problem ◽  
Optimal Stopping Times

For i.i.d. random variables in the domain of attraction of a max-stable distribution with discount and observation costs we determine asymptotic approximations of the optimal stopping values and asymptotically optimal stopping times. The results are based on Poisson approximation of related embedded planar point processes. The optimal stopping problem for the limiting Poisson point processes can be reduced to differential equations for the boundaries. In several cases we obtain numerical solutions of the differential equations. In some cases the analysis allows us to obtain explicit optimal stopping values. This approach thus leads to approximate solutions of the optimal stopping problem of discrete time sequences.

scholarly journals Double Optimal Stopping in the Fishing Problem

2009 ◽  
Vol 46 (02) ◽  
pp. 415-428
Author(s):  
Anna Karpowicz
Keyword(s):  
Dynamic Programming ◽  
Cost Function ◽  
Utility Function ◽  
Optimal Stopping ◽  
Renewal Process ◽  
Fixed Time ◽  
Time Dependent ◽  
Stopping Times ◽  
The Difference ◽  
Optimal Stopping Times

In this paper we consider the following problem. An angler buys a fishing ticket that allows him/her to fish for a fixed time. There are two locations to fish at the lake. The fish are caught according to a renewal process, which is different for each fishing location. The angler's success is defined as the difference between the utility function, which is dependent on the size of the fish caught, and the time-dependent cost function. These functions are different for each fishing location. The goal of the angler is to find two optimal stopping times that maximize his/her success: when to change fishing location and when to stop fishing. Dynamic programming methods are used to find these two optimal stopping times and to specify the expected success of the angler at these times.

Search models

1992 ◽  
Vol 29 (3) ◽  
pp. 605-615 ◽  
Author(s):  
J. A. Bather
Keyword(s):  
Mathematical Models ◽  
Optimal Stopping ◽  
Poisson Processes ◽  
Stopping Rules ◽  
Stopping Times ◽  
Oil Exploration ◽  
Search Models ◽  
Number Of Components ◽  
Optimal Stopping Rules ◽  
Optimal Stopping Times

Mathematical models have been proposed for oil exploration and other kinds of search. They can be used to estimate the amount of undiscovered resources or to investigate optimal stopping times for the search. Here we consider a continuous search for hidden objects using a model which represents the number and values of the objects by mixtures of Poisson processes. The flexibility of the model and its complexity depend on the number of components in the mixture. In simple cases, optimal stopping rules can be found explicitly and more general qualitative results can sometimes be obtained.

scholarly journals Discrete-type approximations for non-Markovian optimal stopping problems: Part I

2019 ◽  
Vol 56 (4) ◽  
pp. 981-1005 ◽  
Author(s):  
Dorival Leão ◽  
Alberto Ohashi ◽  
Francesco Russo
Keyword(s):  
Brownian Motion ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Rates Of Convergence ◽  
Stopping Times ◽  
Full Generality ◽  
Optimal Values ◽  
Optimal Stopping Problems ◽  
Optimal Stopping Times ◽  
Discrete Type

AbstractWe present a discrete-type approximation scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy suitable variational inequalities which allow us to construct $\varepsilon$ -optimal stopping times and optimal values in full generality. Explicit rates of convergence are presented for optimal values based on reward functionals of path-dependent stochastic differential equations driven by fractional Brownian motion. In particular, the methodology allows us to design concrete Monte Carlo schemes for non-Markovian optimal stopping time problems as demonstrated in the companion paper by Bezerra et al.

Search models

1992 ◽  
Vol 29 (03) ◽  
pp. 605-615 ◽  
Author(s):  
J. A. Bather
Keyword(s):  
Mathematical Models ◽  
Optimal Stopping ◽  
Poisson Processes ◽  
Stopping Rules ◽  
Stopping Times ◽  
Oil Exploration ◽  
Search Models ◽  
Number Of Components ◽  
Optimal Stopping Rules ◽  
Optimal Stopping Times

Mathematical models have been proposed for oil exploration and other kinds of search. They can be used to estimate the amount of undiscovered resources or to investigate optimal stopping times for the search. Here we consider a continuous search for hidden objects using a model which represents the number and values of the objects by mixtures of Poisson processes. The flexibility of the model and its complexity depend on the number of components in the mixture. In simple cases, optimal stopping rules can be found explicitly and more general qualitative results can sometimes be obtained.

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