  Supermartingales are here defined on a non-probabilistic setting and can be
interpreted solely in terms of superhedging operations. The classical
expectation operator is replaced by a pair of subadditive operators one of them
providing a class of null sets and the other one acting as an outer integral.
These operators are motivated by a financial theory of no-arbitrage pricing.
Such a setting extends the classical stochastic framework by replacing the path
space of the process by a trajectory set, while also providing a
financial/gambling interpretation based on the notion of superhedging. The
paper proves analogues of the following classical results: Doob's
supermartingale decomposition and Doob's pointwise convergence theorem for
nonnegative supermartingales. The approach shows how linearity of the
expectation operator can be circumvented and how integrability properties in
the proposed setting lead to the special case of (hedging) martingales while no
integrability conditions are required for the general supermartingale case.
