TY - JOUR
T1 - Variance optimal stopping for geometric Levy processes
AU - Gad, Kamille Sofie Tågholt
AU - Pedersen, Jesper Lund
PY - 2015/3/1
Y1 - 2015/3/1
N2 - The main result of this paper is the solution to the optimal stopping problem of maximizing the variance of a geometric Lévy process. We call this problem the variance problem. We show that, for some geometric Lévy processes, we achieve higher variances by allowing randomized stopping. Furthermore, for some geometric Lévy processes, the problem has a solution only if randomized stopping is allowed. When randomized stopping is allowed, we give a solution to the variance problem. We identify the Lévy processes for which the allowance of randomized stopping times increases the maximum variance. When it does, we also solve the variance problem without randomized stopping.
AB - The main result of this paper is the solution to the optimal stopping problem of maximizing the variance of a geometric Lévy process. We call this problem the variance problem. We show that, for some geometric Lévy processes, we achieve higher variances by allowing randomized stopping. Furthermore, for some geometric Lévy processes, the problem has a solution only if randomized stopping is allowed. When randomized stopping is allowed, we give a solution to the variance problem. We identify the Lévy processes for which the allowance of randomized stopping times increases the maximum variance. When it does, we also solve the variance problem without randomized stopping.
U2 - 10.1239/aap/1427814584
DO - 10.1239/aap/1427814584
M3 - Journal article
SN - 0001-8678
VL - 47
SP - 128
EP - 145
JO - Advances in Applied Probability
JF - Advances in Applied Probability
IS - 1
ER -