Quasiconvex Cash Subadditivity Risk Measure for Portfolios

Abstract:

In this paper, quasiconvex cash subadditivity risk measures for portflios is studied. We propose the concept of quasiconvex cash subadditivity risk measures for portflios and provide a dual representation.Which is more flexible than the one introduced by Cerreia-Vioglio and Maccheroni and Marinacci (2011).

• Periodical: Advanced Materials Research (Volumes 989-994)
• Pages: 5241-5244
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.989-994.5241
• Online since: July 2014
• Authors: Hong Wei Liu*, Cai Bo Xiao
• Keywords: Cash Subadditivity, Product Space, Quasiconvexity, Risk Measures

References

[1] Artzner, P., Delbaen, F., Eber, J. M. and Heath, D., Coherent measures of risk, Mathematical Finance , Vol. 9 (1999) No3, pp.203-228.

DOI: 10.1111/1467-9965.00068

[2] Artzner, P., Delbaen, F., Eber, J.M. and Heath, D., Coherent multiperiod risk adjusted values and Bellman's principle, Annals of Operations Research, Vol. 152 (2007) No. 1, pp.5-22, (2007).

DOI: 10.1007/s10479-006-0132-6

[3] Burgert, C., Ruschendorf, L., consistent risk measures for portfolio vectors, Insurance: Mathematics and Economics, Vol. 38 (2006) No. 2, pp.289-297.

DOI: 10.1016/j.insmatheco.2005.08.008

[4] EL Karoui N, Ravanelli C. Cash subadditive risk measures and Interest rate ambiguity. Mathematical Finance, Vol. 19 (2009) No. 4, pp.561-90.

DOI: 10.1111/j.1467-9965.2009.00380.x

[5] Cerreia-Vioglio.S., Maccheroni.F. and Marinacci.M., Risk measures: rationality and diversification, Mathematical Finance, Vol. 21(2011) No. 4, pp.743-774.

DOI: 10.1111/j.1467-9965.2010.00450.x

[6] Kratschmer V. Robust representation of convex risk measures by probability measures. Finance Stochastics , Vol. 9 (2005) No. 4, pp.597-608.

DOI: 10.1007/s00780-005-0160-0

[7] Burgert, C., Ruschendorf, L., consistent risk measures for portfolio vectors, Insurance: Mathematics and Economics, Vol. 38 (2006) No. 2, pp.289-297.

DOI: 10.1016/j.insmatheco.2005.08.008

[8] Cascos, I., Molchanov, I., Multivariate risks and depth-trimmed regions, Finance Stochastics Vol. 11(2007) No. 3, pp.373-397.

DOI: 10.1007/s00780-007-0043-7

[9] Föllmer, H. and Schied, A., Robust preferences and convex measures of risk , (Advances in Finance and Stochastic), pp.39-56. Berlin Heidelberg New York: Springer 2002a.

DOI: 10.1007/978-3-662-04790-3_2

[10] Föllmer, H. and Schied, A., Convex measures of risk and trading constraints, Finance and Stochastics, Vol. 6(2002b), pp.429-447.

DOI: 10.1007/s007800200072

[11] Föllmer, H. and Schied, A., Stochastic Finance: An introduction in discrete time, 2nd ed, De Gruyter Studies in Mathematics 27, (2004).

DOI: 10.1515/9783110198065

[12] Frittelli, M. and Rosazza Gianin, E., Putting order in risk measures, Journal of Banking and Finance, Vol. 26(2002) No. 7, pp.1473-1486.

DOI: 10.1016/s0378-4266(02)00270-4

[13] Frittelli,M., and G. Scandolo, Risk measures and capital requirement for processes, Mathematics Finance, Vol. 16(2005) No. 4, pp.589-612.

DOI: 10.1111/j.1467-9965.2006.00285.x

[14] Kulikov A.V., Multidimensional coherent and convex risk measures, Theory Probab. Appl, Vol. 52 (2008) No. 4, pp.614-635.

DOI: 10.1137/s0040585x97983262

[15] Hamel, A.H., Heyde, F., Duality for set-valued measures of risk, SIAM J. Finan. Math, Vol. 1 (2010) No. 1, pp.66-95.

DOI: 10.1137/080743494

[16] Ludger Ruschendorf, Mathematical Risk Analysis, Springer, (2013).

[17] Deprez, O., Gerber, Hans U., On convex principles of premium calculation, Insurance: Mathematics and Economics, Vol. 4 (1985) No. 3, pp.179-189.

DOI: 10.1016/0167-6687(85)90014-9

[18] Acciaio B, Follmer H, Penner I. Risk assessment for uncertain cash flows: model ambiguity, discounting ambiguity, and the role of bubbles. Financ Stoch, Vol. 16 (2012) No. 4, pp.669-709.

DOI: 10.1007/s00780-012-0176-1