Optimal Stopping Constants
نویسنده
چکیده
k) , t h e n t h e o p t i m a l s t r a t e g y i s t o r e j e c t t h e fi r s t m − 1 a p p l i c a n t s a n d a c c e p t t h e n e x t c a n d i d a t e , w h e r 1 ] c a l c u l a t e d t h e a s y m p t o t i c p r o b a b i l i t y o f s u c c e s s t o b e [ 1 2 ,
منابع مشابه
Optimal Stopping Inequalities for the Integral of Brownian Paths
for all stopping times for B , and all p > 0 , where Ap and Bp are numerical constants. Although the best values for the constants Ap and Bp in (1.1) are found below too, in most of the cases it is much easier to evaluate E( ) rather than E( 1+p=2) . In this paper we shall answer the question on how the inequality (1.1) can be optimally modified if the quantity E( 1+p=2) is replaced by a functi...
متن کاملOptimally Stopping the Sample Mean of a Wiener Process with an Unknown Drift
It is well-known that optimally stopping the sample mean W(t)/t of a standard Wiener process is associated with a square root boundary. It is shown that when W(t) is replaced by X(t)=W(t)+Ot with () normally distributed N(JL,(]2) and independently of the Wiener process, the optimal stopping problem is equivalent to the time-truncated version of the original problem. It is also shown that the pr...
متن کاملMixing Times for Uniformly Ergodic Markov Chains
Consider the class of discrete time, general state space Markov chains which satist)' a "'uniform ergodicity under sampling" condition. There are many ways to quantify the notion of "mixing time", i.e., time to approach stationarity from a worst initial state. We prove results asserting equivalence (up to universal constants) of different quantifications of mixing time. This work combines three...
متن کاملOn a Class of Optimal Stopping Problems with Mixed Constraints
The odds-strategy solves a certain class of sequential decision problems. Although, as we will show, the result needs only elementary tools, it is remarkable in several aspects. Indeed, the corresponding solution algorithm (odds-algorithm) has the property that it yields the optimal strategy and optimal value simultaneously, and that it is optimal itself, that is, no other solution algorithm ca...
متن کاملMaximal Inequalities for Reflected Brownian Motion with Drift
Let = (t) t0 denote the unique strong solution of the equation d t = 0 sign(t) dt + dB t satisfying 0 = 0 , where > 0 and B = (B t) t0 is a standard Brownian motion. Then jj = (j t j) t0 is known to be a realisation of the reflected Brownian motion with drift 0. Using this representation we show that there exist universal constants c 1 > 0 and c 2 > 0 such that c 1 E H () E max 0t j t j c 2 E H...
متن کامل