The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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THE MAXIMAL PRIOR SET IN THE REPRESENTATION OF COHERENT RISK MEASURE

  • Kim, Ju Hong (Department of Mathematics, Sungshin Women's University)
  • Received : 2016.09.11
  • Accepted : 2016.10.04
  • Published : 2016.11.30
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Abstract

The set of priors in the representation of coherent risk measure is expressed in terms of quantile function and increasing concave function. We show that the set of prior, $\mathcal{Q}_c$ in (1.2) is equal to the set of $\mathcal{Q}_m$ in (1.6), as maximal representing set $\mathcal{Q}_{max}$ defined in (1.7).

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References

  1. Z. Chen, T. Chen & M. Davison: Choquet expectation and Peng's g-expectation. The Annals of Probability 33 (2005), 1179-1199. https://doi.org/10.1214/009117904000001053
  2. G. Choquet: Theory of capacities. Ann. Inst. Fourier (Grenoble) 5 (1953), 131-195.
  3. H. Follmer & A. Schied: Stochastic Finance: An introduction in discrete time. Walter de Gruyter, Berlin, 2004.
  4. J.H. Kim: The set of priors in the representation of Choquet expectation when a capacity is submodular. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 22 (2015), 333-342.
  5. S. Kusuoka: On law-invariant coherent risk measures, in Advances in Mathematical Economics. Vol. 3, editors Kusuoka S. and Maruyama T., pp. 83-95, Springer, Tokyo, 2001.
  6. S. Peng: Backward SDE and related g-expectation, backward stochastic DEs. Pitman 364 (1997), 141-159.
  7. G.Ch. Plug & W. Romisch: Modeling, Measuring and Managing Risk. World Scientific Publishing Co., London, 2007.
  8. Zengjing Chen & Larry Epstein: Ambiguity, risk and asset returns in continuous time. Econometrica 70 (2002), 1403-1443. https://doi.org/10.1111/1468-0262.00337