With the aid of authorities, discuss the doctrine of subrogation in the law of insurance.

The doctrine of subrogation in insurance law refers to the right of an insurance company to step into the shoes of the insured, after settlement of a claim, in order to recover from a third party responsible for the loss. This is a fundamental principle of all insurance contracts, designed to prevent the insured from recovering more than the actual amount of the loss.

The principle of subrogation was established in the case of Castellain v Preston (1883) where it was held that the insurer, having indemnified the insured, is entitled to take over all the rights and remedies of the insured whether they are against the insurer or third parties.

In the case of Banque Financiere de la Cite v Westgate Insurance Co Ltd (1990), it was held that the right of subrogation arises immediately upon the insurer paying for the loss. The insurer is then entitled to use the insured's name to sue the third party to recover the amount of the loss.

The doctrine of subrogation is also subject to certain limitations. For instance, an insurer cannot exercise its rights of subrogation against its own insured. This was established in the case of Yorkshire Insurance Co Ltd v Nisbet Shipping Co Ltd (1962).

In conclusion, the doctrine of subrogation is a fundamental principle in insurance law that allows an insurer to recover the amount of a loss from a third party responsible for the loss, after the insurer has indemnified the insured. This principle is subject to certain limitations and is based on the idea that the insured should not recover more than the actual amount of the loss.