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Convex ordering of Esscher and minimal entropy martingale measures for discrete time models

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Fabio Bellini

    (Milano Bicocca University, Department of Quantitative Methods)

  • Carlo Sgarra

    (Technical University of Milan, Department of Mathematics “F. Brioschi”)

Abstract

We recall and extend some sufficient conditions for the convex comparison of martingale measures in a one period setting, based on the elasticity of the pricing kernel. We show that the minimal entropy martingale measure (MEMM) and the Esscher martingale measure are comparable in the convex order, and which one is dominating depends on the sign of the risk premium on the underlying. If it is positive, then the MEMM gives a lower price to each convex payoff. We show how the comparison result can be extended to the multiperiod i.i.d. case and discuss the problems related to the general, non i.i.d. case, proving a Lemma that links one period comparison with multi period comparison under more general assumptions.

Suggested Citation

  • Fabio Bellini & Carlo Sgarra, 2012. "Convex ordering of Esscher and minimal entropy martingale measures for discrete time models," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 27-34, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2342-0_4
    DOI: 10.1007/978-88-470-2342-0_4
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