March 2014 On optimal terminal wealth problems with random trading times and drawdown constraints
Ulrich Rieder, Marc Wittlinger
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Adv. in Appl. Probab. 46(1): 121-138 (March 2014). DOI: 10.1239/aap/1396360106


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.


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Ulrich Rieder. Marc Wittlinger. "On optimal terminal wealth problems with random trading times and drawdown constraints." Adv. in Appl. Probab. 46 (1) 121 - 138, March 2014.


Published: March 2014
First available in Project Euclid: 1 April 2014

zbMATH: 1286.93207
MathSciNet: MR3189051
Digital Object Identifier: 10.1239/aap/1396360106

Primary: 93E20
Secondary: 60G51 , 90C40 , 91B28

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

Rights: Copyright © 2014 Applied Probability Trust


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Vol.46 • No. 1 • March 2014
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