What is optimism in the genuine, that is, in the philosophical, sense?
The blog format and my own laziness precluding a history of the term's usage, excepting a vague memory of Leibniz's philosophy, I will hazard the following statement:
Optimism is the long, hard (and at times painful) coming to realisation that the world as it is and our own being-in-that-world - including our financial, familial, social, creative situation - is optimal, all things considered, that is, taken into consideration, pondered over and scrutinised.
Someone would be an optimist when he or she feels, i.e., intuits, that his or her being-in-the-world, despite what may at first appear rationally in a cogitating sense, is in an optimal and optimum state given both his own being and the world he or she inhabits (on the topic of habitation see my post How to Become Master of the World).
To know oneself which amounts also to knowing the world since world is already at once readily disclosed and pre-given, i.e. world is disclosed wherever and whenever there is Dasein, human existence, (or, in my language, 'the world is in us who in-habit it' - see aforementioned post), is part of optimistic drive to reach the realisation that yes, all things considered, my life is optimal given both my nature which I have come to know and the spiritual world that is disclosed to me in everyday-ness which I also have come to know.
The affirmation and internalisation of Eternal Recurrence - that I want my life to recur forever in the same way - would be part of this optimistic drive.
Eternal Recurrence as the optimally optimistic conception of time's, that is, Dasein's, circular movement.
P.S. The virtuous circle of optimistic thought, as I see it, is encapsulated, in part, by the formulation in Lord of the Rings
"Where there's life, there's hope."and, in part, by the converse, "where there's hope, there's life."
Thus, as long as there is life, there is hope, and provided one is hopeful then life is assured.
[For more on 'optimism' see later writing Psychological Effects of Ideals & Utopias]