DOI QR코드

DOI QR Code

THE PRIOR SET TAKING A MAXIMAL SCENARIO IN THE REPRESENTATION OF COHERENT RISK MEASURE

  • Kim, Ju Hong (Department of Mathematics, Sungshin Women's University)
  • Received : 2017.09.02
  • Accepted : 2017.11.27
  • Published : 2018.02.28

Abstract

It is proved that 'maximum' is actually attained in the following risk measure representation $${\rho}_m(X)={max \atop Q{\in}Q_m}E_Q[-X]$$.

Keywords

References

  1. Z. Chen, T. Chen & M. Davison: Choquet expectation and Peng's g-expectation. The Ann. Probab. 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. K. Floret: Weakly compact sets. Lecture Notes in Math. 801, Springer-Verlag, Berlin, 1980.
  4. H. Follmer & A. Schied: Stochastic Finance: An introduction in discrete time. Walter de Gruyter, Berlin, 2004.
  5. 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.
  6. 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.
  7. S. Peng: Backward SDE and related g-expectation, backward stochastic DEs. Pitman 364 (1997), 141-159.
  8. G.Ch. Plug & W. Romisch: Modeling, Measuring and Managing Risk. World Scientific Publishing Co., London, 2007.
  9. Z. Chen & L. Epstein: Ambiguity, risk and asset returns in continuous time. Econo metrica 70 (2002), 1403-1443. https://doi.org/10.1111/1468-0262.00337