Advances in Applied Probability

On optimal terminal wealth problems with random trading times and drawdown constraints

Ulrich Rieder and Marc Wittlinger

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Abstract

We consider an investment problem where observing and trading are only possible at random times. In addition, we introduce drawdown constraints which require that the investor's wealth does not fall under a prior fixed percentage of its running maximum. The financial market consists of a riskless bond and a stock which is driven by a Lévy process. Moreover, a general utility function is assumed. In this setting we solve the investment problem using a related limsup Markov decision process. We show that the value function can be characterized as the unique fixed point of the Bellman equation and verify the existence of an optimal stationary policy. Under some mild assumptions the value function can be approximated by the value function of a contracting Markov decision process. We are able to use Howard's policy improvement algorithm for computing the value function as well as an optimal policy. These results are illustrated in a numerical example.

Article information

Source
Adv. in Appl. Probab., Volume 46, Number 1 (2014), 121-138.

Dates
First available in Project Euclid: 1 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.aap/1396360106

Digital Object Identifier
doi:10.1239/aap/1396360106

Mathematical Reviews number (MathSciNet)
MR3189051

Zentralblatt MATH identifier
1286.93207

Subjects
Primary: 93E20: Optimal stochastic control
Secondary: 60G51: Processes with independent increments; Lévy processes 90C40: Markov and semi-Markov decision processes 91B28

Keywords
Portfolio optimization illiquid market random trading time drawdown constraint limsup Markov decision process Howard's policy improvement algorithm Lévy process

Citation

Rieder, Ulrich; Wittlinger, Marc. On optimal terminal wealth problems with random trading times and drawdown constraints. Adv. in Appl. Probab. 46 (2014), no. 1, 121--138. doi:10.1239/aap/1396360106. https://projecteuclid.org/euclid.aap/1396360106


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