The purpose of life is the struggle for virtue
Stoics had very little patience with claims that happiness was the goal of life. Instead they emphasized eudaimonia, a good life lived well in accordance with nature. Such a life is not measured by transient mental states like happiness or misery; nor by the temporary satisfaction in achieving a goal or worldly success. Rather, the good life is a life devoted to the struggle for virtue and virtue is a necessary and a sufficient condition for happiness.
Unfortunately the actually arguments for this position are lost to time. We do know Stoics held this position because it was widely criticized during the Hellenic period. Their great rivals, the Epicureans for example, held happiness was the absence from physical pain and the pursuit of pleasure.
Happiness on the Rack.
If virtue alone is sufficient for happiness, would a virtuous Stoic be happy during torture? Surprisingly Stoics answer that yes a Stoic would be happy during torture. A brief argument in favour of this position can be found in Ciceros book V of Tusculan Disputations:
[But will the wise man be terribly afraid of pain?] For pain is the chief obstacle of our view; it points its fiery darts, it threatens to undermine fortitude, greatness of souls and patience. Will virtue then have to give way to pain, will the happy life of the wise and steadfast man yield to it? What degradation great Gods of heaven! Spartan boys utter no cry when their bodies are mangled with painful blows; I have seen with my own eyes troops of youngsters in Lacedaemon fighting with inconceivable obstinacy using fists and feet and nails and even teeth to the point of losing their lives rather than admit defeat. What barbarous country more rude and wild than India? Yet amongst its people those, to begin with, who are reckoned sages pass their lives unclad and endure without show of pain the snows of the Hindu Kush and the rigour of winter, and when they throw themselves voluntarily into the flames they let themselves by burnt without a moan; whilst the women in Indian, if the husband of any of them dies, compete with one another to decide whom the husband loved best; and she who is victorious accompanied by her relatives goes joyfully to join her husband on the funeral pyre; the conquered one sadly quits the field.[..]
But let us check our elegance and return to the point at which we digressed. Happy life will give itself, I say, to torture, and following in the train of justice, temperance and above all of fortitude, of greatness of soul and patience will not halt at the sight of the face of the executioner, and, when all the virtues, while the soul remains undaunted, pass on to face torment, it will not stay behind outside the doors, as I have said, and, threshold of the prison. [..] For the Stoics indeed the conclusion is easy, since they hold it the sovereign good to live according to nature and in harmony with nature, seeing that not only is this the wise mans settled duty but also it lies in his power, and so for them it follows necessarily that where a man has the chief good in his power, he also has the power of happy life : thus the life of the wise is rendered happy always.