Advanced search
Publication Cover
Stochastic Analysis and Applications Volume 35, 2017 - Issue 4
Submit an article Journal homepage
124
Views
1
CrossRef citations to date
0
Altmetric
Article

Representation and approximation of convex dynamic risk measures with respect to strong–weak topologies

Ramin OkhratiMathematical Sciences, University of Southampton, Southampton, UKCorrespondence[email protected]
&
Hirbod AssaInstitute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool, UK
Pages 604-614 | Received 10 Oct 2016, Accepted 28 Jan 2017, Published online: 17 Mar 2017

References

  • Artzner, P., Delbaen, F., Eber, J.-M., and Heath, D. 1999. Coherent measures of risk. Math. Finance 9(3):203–228.
  • Assa, H. 2011. Lebesgue property of convex risk measures for bounded càdlàg. Methods Appl. Anal. 18(3):335–349.
  • Balbás, A., Balbás, B., and Balbás, R. 2010. Minimizing measures of risk by saddle point conditions. J. Comput. Appl. Math. 234(10):2924–2931.
  • Brezis, H. 2011. Functional analysis, Sobolev Spaces and Partial Differential Equations. New York: Universitext Springer.
  • Cerreia-Vioglio, S., Maccheroni, F., and Marinacci, M., and Montrucchio, L. 2011. Complete monotone quasiconcave duality. Math. Oper. Res. 36(2):321–339.
  • Cerreia-Vioglio, S., Maccheroni, F., Marinacci, M., and Montrucchio, L. 2011. Risk measures: rationality and diversification. Math. Finance 21(4):743–774.
  • Cheridito, P., and Delbaen, F., and Kupper, M. 2011. Dynamic monetary risk measures for bounded discrete-time processes. Electron. J. Probab. 11(3):57–106.
  • Cheridito, P., and Kupper, M. 2011. Composition of time-consistent dynamic monetary risk measures in discrete time. Int. J. Theor. Appl. Finance 14(1):137–162.
  • Detlefsen, K., and Scandolo, G. 2005. Conditional and dynamic convex risk measures. Finance Stoch. 9(4):539–561.
  • El Karoui, N., and Ravanelli, C. 2009. Cash subadditive risk measures and interest rate ambiguity. Math. Finance 19(4):561–590.
  • Föllmer, H., and Schied, A. 2011. Stochastic Finance: An Introduction in Discrete Time, extended ed. Berlin: Berlin: de Gruyter.
  • Frittelli, M., and Maggis, M. 2011. Dual representation of quasi-convex conditional maps. SIAM J. Financial Math. 2(1):357–382.
  • Frittelli, M., and Maggis, M. 2014. Complete duality for quasiconvex dynamic risk measures on modules of the Lp-type. Stat. Risk Model. 31(1):103–128.
  • Riedel, F. 2004. Dynamic coherent risk measures. Stochastic Process. Appl. 112(2):185–200.
  • Rockafellar, R. 1966. Characterization of the subdifferentials of convex functions. Pacific Journal of Mathematics 17(3):497–510.
  • Zowe, J. 1975. A duality theorem for a convex programming problem in order complete vector lattices. J. Math. Anal. Appl. 50:273–287.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.