COMPOUND POISSON DISORDER PROBLEM WITH UNIFORMLY DISTRIBUTED DISORDER TIME
ÇAĞIN ÜRÜ
M.S. in Industrial Engineering
Advisor: Prof. Dr. Savaş Dayanık
DAY, JULY 22, 2019 AT 10:30 @ EA-409
ABSTRACT
Suppose that arrival rate and jump distribution of a compound Poisson process change suddenly at an unknown and unobservable time. The problem of detecting the change (disorder) as soon as it occurs is known as compound Poisson disorder. In practice, an unfavorable regime shift may require immediate action, and a quickest detection rule can allow the decision maker to react to the change and take the necessary countermeasures in a timely manner.
Dayanık and Sezer [Compound Poisson disorder problem, Math. Oper. Res., vol. 31, no. 4, pp. 649-672, 2006] completely solve the compound Poisson disorder problem assuming a change-point with an exponential prior distribution. Although the exponential prior is convenient when solving the problem, it has flaws when expressing reality due to the memoryless property. Besides, as an informative prior, it fails to represent the case when the decision maker has no prior information on the change-point. Considering these limitations, we assume a uniformly distributed change-point instead in our study. Unlike the exponential prior, the uniform prior has a memory and can be used when the decision maker does not have a strong belief on the change-point. We reformulate the quickest detection problem as a finite-horizon optimal stopping problem for a piecewise-deterministic and Markovian sufficient statistic. With successive approximations, we calculate the value function numerically by using Monte Carlo simulation and Chebyshev interpolation. Studying the sample-paths of the sufficient statistic, we describe an explicit quickest detection rule and provide numerical examples for our solution method.