## Advances in Applied Probability

- Adv. in Appl. Probab.
- Volume 47, Number 1 (2015), 128-145.

### Variance optimal stopping for geometric Lévy processes

Kamille Sofie Tågholt Gad and Jesper Lund Pedersen

#### Abstract

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.

#### Article information

**Source**

Adv. in Appl. Probab., Volume 47, Number 1 (2015), 128-145.

**Dates**

First available in Project Euclid: 31 March 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.aap/1427814584

**Digital Object Identifier**

doi:10.1239/aap/1427814584

**Mathematical Reviews number (MathSciNet)**

MR3327318

**Zentralblatt MATH identifier**

1310.60041

**Subjects**

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Secondary: 90C20: Quadratic programming

**Keywords**

Variance criterion variance optimal stopping geometric Lévy process quadratic optimal stopping

#### Citation

Gad, Kamille Sofie Tågholt; Pedersen, Jesper Lund. Variance optimal stopping for geometric Lévy processes. Adv. in Appl. Probab. 47 (2015), no. 1, 128--145. doi:10.1239/aap/1427814584. https://projecteuclid.org/euclid.aap/1427814584