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Approximating sums of products of dependent random variables

Author

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  • Gajek, Lesław
  • Krajewska, Elżbieta

Abstract

Stochastic approximation of a given time series {∑j=1kXjYj} by a linear combination of simpler sequences {∑j=1kXj} and {∑j=1kYj} is treated uniformly over k∈{1,…,n}. A maximal inequality is proven in order to find a sharp bound on Value-at-Risk of max1≤k≤n|∑j=1kXjYj|.

Suggested Citation

  • Gajek, Lesław & Krajewska, Elżbieta, 2020. "Approximating sums of products of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:stapro:v:164:y:2020:i:c:s0167715220301061
    DOI: 10.1016/j.spl.2020.108803
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    References listed on IDEAS

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    4. John Y. Campbell & Robert J. Shiller & Luis M. Viceira, 2009. "Understanding Inflation-Indexed Bond Markets," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 40(1 (Spring), pages 79-138.
    5. Shanchao, Yang, 2006. "Moment inequalities for sums of products of independent random variables," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1994-2000, December.
    6. Gajek, Lesław & Krajewska, Elżbieta, 2013. "A new immunization inequality for random streams of assets, liabilities and interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 624-631.
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