This paper provides the notion of ‘robust survival’ to examine the existence of equilibrium in a general equilibrium model with incomplete markets (GEI model). The GEI model satisfies robust survival if for each agent, any non-optimal choice is dominated by a choice that can be slightly shaken to be budget-feasible in the wake of slight price-endowment variations. The new survival condition differs from the GEI irreducibility of Gottardi and Hens (1996) in the ability to explain the presence of agents with the cheap initial endowments in equilibrium. Both survival conditions can be rather complementary in investigating the effect of financial innovation on the welfare of agents who lack the cheaper consumption property in the pre-innovation economy. We take an example where the economy satisfies the new survival condition and is not GEI irreducible because an agent has the cheap initial endowments. The economy becomes GEI irreducible when asset markets are completed through financial innovation. This means the agent with the cheap endowments in the pre-innovation economy gains access to cheaper consumptions in the post-innovation economy.