Journal of Applied Probability

A remark on optimal variance stopping problems

Bruno Buonaguidi

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Abstract

In an optimal variance stopping problem the goal is to determine the stopping time at which the variance of a sequentially observed stochastic process is maximized. A solution method for such a problem has been recently provided by Pedersen (2011). Using the methodology developed by Pedersen and Peskir (2012), our aim is to show that the solution to the initial problem can be equivalently obtained by constraining the variance stopping problem to the expected size of the stopped process and then by maximizing the solution to the latter problem over all the admissible constraints. An application to a diffusion process used for modeling the dynamics of interest rates illustrates the proposed technique.

Article information

Source
J. Appl. Probab., Volume 52, Number 4 (2015), 1187-1194.

Dates
First available in Project Euclid: 22 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.jap/1450802762

Digital Object Identifier
doi:10.1239/jap/1450802762

Mathematical Reviews number (MathSciNet)
MR3439181

Zentralblatt MATH identifier
1334.60061

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 62L15: Optimal stopping [See also 60G40, 91A60] 90C20: Quadratic programming

Keywords
Constrained and unconstrained variance optimal stopping problems diffusion process interest rate nonlinear optimal stopping problem

Citation

Buonaguidi, Bruno. A remark on optimal variance stopping problems. J. Appl. Probab. 52 (2015), no. 4, 1187--1194. doi:10.1239/jap/1450802762. https://projecteuclid.org/euclid.jap/1450802762


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