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Constrained Optimization With Respect To Stochastic Dominance: Application To Portfolio Insurance

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  • Nicole El Karoui
  • Asma Meziou

Abstract

We are concerned with a classic portfolio optimization problem where the admissible strategies must dominate a floor process on every intermediate date (American guarantee). We transform the problem into a martingale, whose aim is to dominate an obstacle, or equivalently its Snell envelope. The optimization is performed with respect to the concave stochastic ordering on the terminal value, so that we do not impose any explicit specification of the agent's utility function. A key tool is the representation of the supermartingale obstacle in terms of a running supremum process. This is illustrated within the paper by an explicit example based on the geometric Brownian motion.

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  • Nicole El Karoui & Asma Meziou, 2006. "Constrained Optimization With Respect To Stochastic Dominance: Application To Portfolio Insurance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 103-117, January.
    • Handle: RePEc:bla:mathfi:v:16:y:2006:i:1:p:103-117
    DOI: 10.1111/j.1467-9965.2006.00263.x
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    Cited by:

    1. Lijun Bo & Huafu Liao & Xiang Yu, 2020. "Optimal Tracking Portfolio with A Ratcheting Capital Benchmark," Papers 2006.13661, arXiv.org, revised Apr 2021.
    2. Leilei Zhang & Tito Homem-de-Mello, 2017. "An Optimal Path Model for the Risk-Averse Traveler," Transportation Science, INFORMS, vol. 51(2), pages 518-535, May.
    3. Lingjiong Zhu, 2015. "Short maturity options for Azéma–Yor martingales," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-32, December.
    4. Nicole El Karoui & Asma Meziou, 2008. "Max-Plus decomposition of supermartingales and convex order. Application to American options and portfolio insurance," Papers 0804.2561, arXiv.org.
    5. Lijun Bo & Yijie Huang & Xiang Yu, 2023. "Stochastic control problems with state-reflections arising from relaxed benchmark tracking," Papers 2302.08302, arXiv.org, revised Apr 2024.
    6. Vladimir Cherny & Jan Obloj, 2013. "Optimal portfolios of a long-term investor with floor or drawdown constraints," Papers 1305.6831, arXiv.org.
    7. Zhenyu Cui, 2013. "Stochastic areas of diffusions and applications in risk theory," Papers 1312.0283, arXiv.org.
    8. Lijun Bo & Yijie Huang & Xiang Yu, 2023. "An extended Merton problem with relaxed benchmark tracking," Papers 2304.10802, arXiv.org, revised Jul 2024.
    9. Jun Sekine, 2012. "Long-term optimal portfolios with floor," Finance and Stochastics, Springer, vol. 16(3), pages 369-401, July.

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