Is it permissible for a Muslim to say "I am poor" to a rich person who boasts about his possessions, while he [the Muslim] owns nothing?

There is no harm in showing poverty, for poverty is not a defect to be ashamed of. Allah has refuted those who thought that wealth is a sign of honor and poverty is a sign of humiliation, saying: "As for man, when his Lord tries him and [thus] is generous to him and favors him, he says, 'My Lord has honored me.' But when He tries him and restricts his provision, he says, 'My Lord has humiliated me.' No!" [Al-Fajr: 15-16]. So, wealth is not due to the merit of its owner, nor is poverty due to his insignificance; rather, it is a test. The Prophet, peace be upon him, said about a poor person: "This one is better than an earth full of people like that." The poor person should be self-restrained, content, and not covetous of what others possess, for Allah Almighty says: "And do not extend your eyes toward that by which We have given enjoyment to [various] kinds of them - the splendor of worldly life - that We might test them thereby. And the provision of your Lord is better and more lasting." [Taha: 131]. And the Prophet, peace be upon him, said: "He has succeeded who has embraced Islam, been provided with just enough, and been made content by Allah with what He has given him."