Season swordfish with salt and pepper, then sprinkle with balsamic vinegar, olive oil and lime juice and zest. Cover then refrigerate and marinate for 45 minutes. Simmer the sugar, vinegar, water, salt and spices for 5 minutes, then leave to stand for 30 minutes.
Strain the spice stock and pour into a pot. Lightly fry the pumpkin in olive oil, then add the spice stock little by little and simmer until pumpkin is cooked and sauce reduced.
Leave to cool, then add the apricot jam. Season to taste and serve with the swordfish.