Reports of my death have been greatly exaggerated

I thought it was interesting to compare Alonso and Fernando with Leontes and Paulina, from The Winter's Tale.

When Alonso and his men wash up on shore, Fernando assures his king that the prince Ferdinand is still alive somewhere:

"Francisco: Sir, he may live:
I saw him beat the surges under him,
And ride upon their backs; he trod the water,
Whose enmity he flung aside, and breasted
The surge most swoln that met him; his bold head
'Bove the contentious waves he kept, and oar'd
Himself with his good arms in lusty stroke
To the shore, that o'er his wave-worn basis bow'd,
As stooping to relieve him: I not doubt
He came alive to land."

While Francisco is trying to keep Alonso's hopes up, Paulina finds every opportunity she can to remind Leontes that Hermione is dead and that it's his fault:

"Paulina: This news is mortal to the queen: look down
And see what death is doing. ...

but the last,—O lords,
When I have said, cry 'woe!' the queen, the queen,
The sweet'st, dear'st creature's dead,
and vengeance for't
Not dropp'd down yet. ...

I say she's dead; I'll swear't. If word nor oath
Prevail not, go and see ..."

What's funny is that in both cases, the character who is presumably dead is actually still alive.

We've spent time in class talking about Paulina's motivation in reminding Leontes that his queen is dead. But why is Fernando reassuring King Alonso that Ferdinand is alive? Is it simply a general optimism? Or is there some other motive, like Paulina had?