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Asymptotic behaviour of mean-quantile efficient portfolios

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Abstract

In this paper we investigate portfolio optimization in the Black–Scholes continuous-time setting under quantile based risk measures: value at risk, capital at risk and relative value at risk. We show that the optimization results are consistent with Merton’s two-fund separation theorem, i.e., that every optimal strategy is a weighted average of the bond and Merton’s portfolio. We present optimization results for constrained portfolios with respect to these risk measures, showing for instance that under value at risk, in better markets and during longer time horizons, it is optimal to invest less into the risky assets.

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References

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Authors and Affiliations

  1. The Mathematical and Computational Finance Laboratory, Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada, T2N 1N4

    Gordana Dmitrašinović-Vidović & Antony Ware

Authors
  1. Gordana Dmitrašinović-Vidović
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  2. Antony Ware
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Corresponding author

Correspondence to Antony Ware.

Additional information

This research was partially supported by the National Science and Engineering Research Council of Canada, and the Mathematics of Information Technology and Complex Systems (MITACS) Network of Centres of Excellence.

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Dmitrašinović-Vidović, G., Ware, A. Asymptotic behaviour of mean-quantile efficient portfolios. Finance Stoch 10, 529–551 (2006). https://doi.org/10.1007/s00780-006-0018-0

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  • DOI: https://doi.org/10.1007/s00780-006-0018-0

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