Re-applying for the same PhD program abroad after finishing it in one's home country? This is a little bit hypothetical question… Let's assume I finished my PhD in math in my country but I am dissatisfied with it (assume I live in a developing country). Also I have enough money and time. Can I apply for a similar PhD program in an another country? Is it theoretically possible?
No, it's generally not possible.  Almost all Ph.D. programs have a rule against admitting someone who already has a research doctorate.  Under special circumstances, one might be admitted as an unfunded Ph.D. student in a completely different field; but in the same field, never.