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A remark on optimal variance stopping problems

Part of: Sequential methods Stochastic processes

Published online by Cambridge University Press:  30 March 2016

Bruno Buonaguidi
Bruno Buonaguidi*
Affiliation:
Bocconi University
*
∗Postal address: Department of Decision Sciences, Bocconi University, Via Roentgen 1, 20136 Milan, Italy. Email address: bruno.buonaguidi@phd.unibocconi.it
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Abstract

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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.

Keywords

Constrained and unconstrained variance optimal stopping problemsdiffusion processinterest ratenonlinear optimal stopping problem

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 62L15: Optimal stopping 90C20: Quadratic programming
Type
Short Communications
Information
Journal of Applied Probability , Volume 52 , Issue 4 , December 2015 , pp. 1187 - 1194
Copyright
Copyright © Applied Probability Trust 2015 

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