Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T13:40:13.670Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on ‘Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options’ by Tankov (2011)

Part of: Distribution theory - Probability Mathematical finance Applications

Published online by Cambridge University Press:  04 February 2016

Carole Bernard ,
Xiao Jiang  and
Steven Vanduffel
Carole Bernard*
Affiliation:
University of Waterloo
Xiao Jiang*
Affiliation:
University of Waterloo
Steven Vanduffel*
Affiliation:
Vrije Universiteit Brussel
*
∗ Postal address: Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo ON, N2L 3G1, Canada.
∗ Postal address: Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo ON, N2L 3G1, Canada.
∗∗∗∗ Postal address: Faculty of Economics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Elsene, Belgium. Email address: steven.vanduffel@vub.ac.be
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Tankov (2011) improved the Fréchet bounds for a bivariate copula when its values on a compact subset of [0, 1]2 are given. He showed that the best possible bounds are quasi-copulas and gave a sufficient condition for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that the bounds are copulas. We also show how this can be useful in portfolio selection. It turns out that finding a copula as a lower bound plays a key role in determining optimal investment strategies explicitly for investors with some type of state-dependent constraints.

Keywords

CopulaFréchet-Hoeffding boundquasi-copulaoptimal portfolio selection

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 62P05: Applications to actuarial sciences and financial mathematics 91G10: Portfolio theory
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 3 , September 2012 , pp. 866 - 875
Copyright
© Applied Probability Trust 

References

Bernard, C. and Vanduffel, S. (2011). Optimal investment under probability constraints. In Proc. 2011 Actuarial and Financial Mathematics Conf., Universa Press, Belgium, pp. 3–14.Google Scholar
Bernard, C., Boyle, P. P. and Vanduffel, S. (2011). Explicit representation of cost-efficient strategies. Working paper. Available at http://dx.doi.org/10.2139/ssrn.1561272.CrossRefGoogle Scholar
Meilijson, I. and Nadas, A. (1979). Convex majorization with an application to the length of critical paths. J. Appl. Prob. 16, 671–677.Google Scholar
Nelsen, R. (2006). An Introduction to Copulas, 2nd edn. Springer, New York.Google Scholar
Rachev, S. T. and Rüschendorf, L. (1994). Solution of some transportation problems with relaxed or additional constraints. SIAM J. Control Optimization 32, 673–689.CrossRefGoogle Scholar
Rachev, S. T. and Rüschendorf, L. (1998). Mass Transportation Problems, Vol. II. Springer, New York.Google Scholar
Rüschendorf, L. (1983). Solution of a statistical optimization problem by rearrangement methods. Metrika 30, 55–61.CrossRefGoogle Scholar
Tankov, P. (2011). Improved Fréchet bounds and model-free pricing of multi-asset options. J. Appl. Prob. 48, 389–403.Google Scholar
Tchen, A. H. (1980). Inequalities for distributions with given margins. Ann. Appl. Prob. 8, 814–827.Google Scholar