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The least squares estimator of random variables under convex operators on LF∞(μ) space

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  • Sun, Chuanfeng
  • Ji, Shaolin
  • Kong, Chuiliu

Abstract

In this paper, the least squares estimator of random variables for a convex operator is investigated on LF∞(μ) space. We adopt much weaker conditions for the convex operator than in Ji et al. (2020) and Sun and Ji (2017). These weaker conditions can also guarantee that the minimax theorem holds. Due to Komlós theorem and the minimax theorem, the existence and uniqueness of the least squares estimator are obtained.

Suggested Citation

  • Sun, Chuanfeng & Ji, Shaolin & Kong, Chuiliu, 2022. "The least squares estimator of random variables under convex operators on LF∞(μ) space," Statistics & Probability Letters, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:stapro:v:181:y:2022:i:c:s0167715221002303
    DOI: 10.1016/j.spl.2021.109268
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    References listed on IDEAS

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    1. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    2. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath & Hyejin Ku, 2007. "Coherent multiperiod risk adjusted values and Bellman’s principle," Annals of Operations Research, Springer, vol. 152(1), pages 5-22, July.
    3. Freddy Delbaen & Shige Peng & Emanuela Rosazza Gianin, 2010. "Representation of the penalty term of dynamic concave utilities," Finance and Stochastics, Springer, vol. 14(3), pages 449-472, September.
    4. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    5. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    6. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704, Decembrie.
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