A state is called insurable if there exists a portfolio x which has a positive return if

Question:

A state is called insurable if there exists a x which has a positive return if state occurs and zero return in any other state, that is,

Show that every state is insurable if and only if rank R = S.

Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...