Research output: Contribution to journal › Article

Abstract

We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often known as the "full information" problem. In this analysis, we obtain asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables becomes large. In the case of distributions with infinite upper bound, the asymptotic behaviour of these statistics depends solely on the algebraic power of the probability distribution decay rate in the upper limit. In the case of densities with finite upper bound, the asymptotic behaviour these statistics depend on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions.

title = "On asymptotics of optimal stopping times",

abstract = "We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often known as the {"}full information{"} problem. In this analysis, we obtain asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables becomes large. In the case of distributions with infinite upper bound, the asymptotic behaviour of these statistics depends solely on the algebraic power of the probability distribution decay rate in the upper limit. In the case of densities with finite upper bound, the asymptotic behaviour these statistics depend on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions.",

author = "Christopher Lustri and Georgy Sofronov",

Research output: Contribution to journal › Article

TY - JOUR

T1 - On asymptotics of optimal stopping times

AU - Lustri, Christopher

AU - Sofronov, Georgy

PY - 2019/4/5

Y1 - 2019/4/5

N2 - We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often known as the "full information" problem. In this analysis, we obtain asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables becomes large. In the case of distributions with infinite upper bound, the asymptotic behaviour of these statistics depends solely on the algebraic power of the probability distribution decay rate in the upper limit. In the case of densities with finite upper bound, the asymptotic behaviour these statistics depend on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions.

AB - We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often known as the "full information" problem. In this analysis, we obtain asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables becomes large. In the case of distributions with infinite upper bound, the asymptotic behaviour of these statistics depends solely on the algebraic power of the probability distribution decay rate in the upper limit. In the case of densities with finite upper bound, the asymptotic behaviour these statistics depend on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions.