There is not in the classical Greek authors, Aristotle and Plato, in particular, a study on the virtue of hope. Is with the gospels and the scholastic philosophy that a knowledge about this virtue is reached.
The theological virtue of hope is a virtue infused by the holy spirit according to the Thomistic school (scholastic philosophy) and one of the seven Christian virtues that are: temperance, fortitude, justice, prudence, faith, Charity and hope.
In the Christian religion, hope is one of the three gifts, together with the justification and faith that are received in the sacrament of Baptism. Faith is accepting the creed and the hope is the trust in receiving the good of the eternal life and the blessings of the beatitudes. The virtue of hope in practice is a virtue that assists us in the concrete difficulties of life. Justification completes the infused virtues and prepares the soul for the life in grace.
The Epistle to the Hebrews tells us about the infused virtues of faith and hope, the letter, although it is from an unknown author, but probably Paul, the epistle is a homily and an exhortation to keep the Faith.
In the lettet the autor expresses: we want each of you to show this same diligence to the very end, so that what you hope for may be fully realized. We do not want you to become lazy, but to imitate those who through faith and patience inherit what has been promised. Hebrews 6:11-12
The author of the epistle to the Hebrews teaches us that this virtue completes and perfects Charity (love for the good or love perfected by the nature of the good) and Faith. Continuing this idea the hope is a spiritual gift (teological concept).
In the epistle the author continues and teach: We have this hope as an anchor for the soul, firm and secure. Hebrews 6:19
In the letter the author talks about hope and teach us that hope implies zeal and patience to achieve the promises of the Beatitudes. Let us remember that the beatitudes besides being the description of God' s plan are promises of blessing, hope seeks the long term, not the short one.
The virtue of hope, although it is understood to orders man to the divine, depends on the life in grace, in essence there is no hope for those who practice error. Hope is not realized in the afterlife, it is realized in the eternal life, which is in essence the true promise of the beatitudes: "This is eternal life, that they may know you the only true God", John 17 :3.