Browsing by Keywords "Optimal stopping"
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Asymptotically optimal Bayesian sequential change detection and identification rules
(2013)We study the joint problem of sequential change detection and multiple hypothesis testing. Suppose that the common distribution of a sequence of i.i.d. random variables changes suddenly at some unobservable time to one of ... 
Compound Poisson disorder problem with uniformly distributed disorder time
(Bilkent University, 201907)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 ... 
Compound poisson disorder problems with nonlinear detection delay penalty cost functions
(2010)The quickest detection of the unknown and unobservable disorder time, when the arrival rate and mark distribution of a compound Poisson process suddenly changes, is formulated in a Bayesian setting, where the detection ... 
Discretetime pricing and optimal exercise of American perpetual warrants in the geometric random walk model
(2013)An American option (or, warrant) is the right, but not the obligation, to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option ... 
Multisource Bayesian sequential binary hypothesis testing problem
(2012)We consider the problem of testing two simple hypotheses about unknown local characteristics of several independent Brownian motions and compound Poisson processes. All of the processes may be observed simultaneously as ... 
Optimal stopping problems for asset management
(2012)An asset manager invests the savings of some investors in a portfolio of defaultable bonds. The manager pays the investors coupons at a constant rate and receives a management fee proportional to the value of the portfolio. ... 
Pricing perpetual Americantype strangle option for merton's jump diffusion process
(Bilkent University, 2014)A stock price Xt evolves according to jump diffusion process with certain parameters. An asset manager who holds a strangle option on that stock, wants to maximize his/her expected payoff over the infinite time horizon. ... 
Riskaverse control of undiscounted transient Markov models
(Society for Industrial and Applied Mathematics, 2014)We use Markov risk measures to formulate a riskaverse version of the undiscounted total cost problem for a transient controlled Markov process. Using the new concept of a multikernel, we derive conditions for a system to ... 
Wiener disorder problem with observations at fixed discrete time epochs
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2010)Suppose that a Wiener process gains a known drift rate at some unobservable disorder time with some zeromodified exponential distribution. The process is observed only at known fixed discrete time epochs, which may not ...