We give analytical bounds on the Value-at-Risk and on convex risk measures for a portfolio of random variables with fixed marginal distributions under an additional positive dependence structure. We show that assuming positive dependence information in our model leads to reduced dependence uncertainty spreads compared to the case where only marginals information is known. In more detail, we show that in our model the assumption of a positive dependence structure improves the best-possible lower estimate of a risk measure, while leaving unchanged its worst-possible upper risk bounds. In a similar way, we de- rive for convex risk measures that the assumption of a negative dependence structure leads to improved upper bounds for the risk while it does not help to increase the lower risk bounds in an essential way. As a result we find that additional assumptions on the dependence structure may result in essentially improved risk bounds.

Reducing model risk via positive and negative dependence assumptions / Valeria Bignozzi; Giovanni Puccetti; Ludger Rüschendorf. - In: INSURANCE MATHEMATICS & ECONOMICS. - ISSN 0167-6687. - STAMPA. - 61:(2015), pp. 17-26. [10.1016/j.insmatheco.2014.11.004]

Reducing model risk via positive and negative dependence assumptions

PUCCETTI, GIOVANNI;
2015

Abstract

We give analytical bounds on the Value-at-Risk and on convex risk measures for a portfolio of random variables with fixed marginal distributions under an additional positive dependence structure. We show that assuming positive dependence information in our model leads to reduced dependence uncertainty spreads compared to the case where only marginals information is known. In more detail, we show that in our model the assumption of a positive dependence structure improves the best-possible lower estimate of a risk measure, while leaving unchanged its worst-possible upper risk bounds. In a similar way, we de- rive for convex risk measures that the assumption of a negative dependence structure leads to improved upper bounds for the risk while it does not help to increase the lower risk bounds in an essential way. As a result we find that additional assumptions on the dependence structure may result in essentially improved risk bounds.
61
17
26
Valeria Bignozzi; Giovanni Puccetti; Ludger Rüschendorf
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/950943
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