A new concept of reliability system and applications in finance

This paper proposes and explores an extension of the usual k-out-of-n systems, where the components of the system are assumed to play different roles in determining its failure and with not necessarily i.i.d. components lifetimes. The theoretical reliability framework is compared with the standard weighted k-out-of-n systems, and it is actually adopted for the development of a financial derivative model whose outcome depends on the crossing of some predefined barriers of a set of assets. More precisely, such a derivative is presented as a coherent system whose components are the assets of the basket.