The Heimskringla on Asmund
Heimskringla > part in the government with his brother Hardaknut. In the same autumn > 51. Murder Of Asmund.
attestation: Asmund was said to be King Svein's sister's son and foster-son, distinguished for boldness but much disliked by the king.
"There was a man called Asmund, who is said to have been King Svein's sister's son, and his foster-son. This Asmund was distinguished among all by his boldness and was much disliked by the king."
attestation: Asmund became ungovernable, committing murder and manslaughter; Svein gave him a fief to manage but Asmund exceeded his allowance and seized royal property.
"When Asmund came to years, and to age of discretion, he became an ungovernable person given to murder and manslaughter. The king was ill pleased at this, and sent him away, giving him a good fief"
attestation: Asmund repeatedly escaped custody and returned to violent plunder, making him a persistent problem for Svein's realm.
"no sooner did Asmund get rid of his chains than he absconded again, gathered together people and men-at-arms and betook himself to plunder, both abroad and at home."