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Quantizations of probability measures and preservation of the convex order

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  • Baker, David M.

Abstract

Two probability measures admit a martingale transition if and only if they are ordered in the convex order (Kellerer, 1972). We show that the commonly used quantization method, L2-quantization, does not have the property of preserving the convex order. We introduce an alternative quantization method and demonstrate that it preserves the convex order. This result has implications concerning the choice of quantization methods for the numerical construction of martingales with specified marginals.

Suggested Citation

  • Baker, David M., 2015. "Quantizations of probability measures and preservation of the convex order," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 280-285.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:280-285
    DOI: 10.1016/j.spl.2015.09.001
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    References listed on IDEAS

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    1. Albin, J.M.P., 2008. "A continuous non-Brownian motion martingale with Brownian motion marginal distributions," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 682-686, April.
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    Cited by:

    1. Benjamin Jourdain & Gilles Pagès, 2022. "Convex Order, Quantization and Monotone Approximations of ARCH Models," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2480-2517, December.

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