Worst-Case Optimal Investment with a Random Number of Crashes

Statistics and Probability Letters, Volume 90, pp. 140-148, July 2014.

Posted: 21 Nov 2013 Last revised: 2 May 2016

See all articles by Christoph Belak

Christoph Belak

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften

Sören Christensen

Gothenburg University

Olaf Menkens

Dublin City University - School of Mathematical Sciences

Date Written: November 24, 2013

Abstract

We study a portfolio optimization problem in a market which is under the threat of crashes. At random times, the investor receives a warning that a crash in the risky asset might occur. We construct a strategy which renders the investor indifferent about an immediate crash of maximum size and no crash at all. We then verify that this strategy outperforms every other trading strategy using a direct comparison approach. We conclude with numerical examples and calculating the costs of hedging against crashes.

Keywords: optimal investment, market crashes, worst-case scenario, financial bubbles

JEL Classification: G11

Suggested Citation

Belak, Christoph and Christensen, Sören and Menkens, Olaf, Worst-Case Optimal Investment with a Random Number of Crashes (November 24, 2013). Statistics and Probability Letters, Volume 90, pp. 140-148, July 2014., Available at SSRN: https://ssrn.com/abstract=2357514 or http://dx.doi.org/10.2139/ssrn.2357514

Christoph Belak (Contact Author)

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften ( email )

Institut fur Mathematik, Sekr. MA 7-1
Strasse des 17. Juni 136
Berlin, 10623
Germany

Sören Christensen

Gothenburg University ( email )

Göteborg, 41296
Sweden

Olaf Menkens

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

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