Note on 'Improved Frechet Bounds and Model-Free Pricing of Multi-Asset Options' by Tankov (2011)
12 Pages Posted: 13 Feb 2012 Last revised: 11 May 2012
Date Written: February 11, 2012
Tankov (2011) improves the Fréchet bounds for a bivariate copula when its values on a compact subset of the unit square are given. He shows that the best possible bounds are quasi-copulas and gives a sufficient condition for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that the bounds are copulas. Next, we show how this can be very 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: bounds, copulas, Frechet Hoeffding bounds, quasi-copula, optimal investment, state dependent constraints
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