TY - JOUR

T1 - Some optimal variance stopping problems revisited with an application to the Italian Ftse-Mib stock index

AU - Buonaguidi, Bruno

AU - Mira, Antonietta

PY - 2018

Y1 - 2018

N2 - Optimal variance stopping (O.V.S.) problems are a new class of optimal stopping problems that differ from the classical ones because of their non linear (quadratic) dependence on the expectation operator. These problems were introduced by Pedersen (2011), who provided an effective solution method and derived the explicit solutions to the O.V.S. problem for some important examples of diffusion processes. In this article, we analyze the examples of Pedersen (2011) in light of the results in Buonaguidi (2015), where an alternative method for solving an O.V.S. problem was developed: this method is based on the solution of a constrained optimal stopping problem, whose maximization, over all the admissible constraints, returns the solution to the O.V.S. problem. Using real data on the Italian Ftse-Mib stock index, we also discuss how the solution to the O.V.S. problem for a geometric Brownian motion can be used in trading strategies.

AB - Optimal variance stopping (O.V.S.) problems are a new class of optimal stopping problems that differ from the classical ones because of their non linear (quadratic) dependence on the expectation operator. These problems were introduced by Pedersen (2011), who provided an effective solution method and derived the explicit solutions to the O.V.S. problem for some important examples of diffusion processes. In this article, we analyze the examples of Pedersen (2011) in light of the results in Buonaguidi (2015), where an alternative method for solving an O.V.S. problem was developed: this method is based on the solution of a constrained optimal stopping problem, whose maximization, over all the admissible constraints, returns the solution to the O.V.S. problem. Using real data on the Italian Ftse-Mib stock index, we also discuss how the solution to the O.V.S. problem for a geometric Brownian motion can be used in trading strategies.

KW - Diffusion processes

KW - Modeling and Simulation

KW - Statistics and Probability

KW - geometric Brownian motion

KW - optimal variance stopping problems

KW - trading strategies

KW - Diffusion processes

KW - Modeling and Simulation

KW - Statistics and Probability

KW - geometric Brownian motion

KW - optimal variance stopping problems

KW - trading strategies

UR - http://hdl.handle.net/10807/133219

UR - http://www.tandf.co.uk/journals/titles/07474946.asp

U2 - 10.1080/07474946.2018.1427979

DO - 10.1080/07474946.2018.1427979

M3 - Article

SN - 0747-4946

VL - 37

SP - 90

EP - 101

JO - Sequential Analysis

JF - Sequential Analysis

ER -