The operation of insurance companies accumulates several risks that should be managed. One of the risk management and containment types is reinsurance. Risks related to reinsurance are the following: fluctuation risk, risk of errors, risk of change, risk of prediction and assessment, subjective risk, and premium delay risk. Reinsurance as the limiting type of fluctuation risk is a transaction, under which one insurance company (reinsurer) agrees to indemnify to another insurance company (transferor) all or part of the losses identified under the insurance policy or a group of insurance policies issued, and for risk mitigation the transferor pays the premium to the reinsurer. The object of the paper is the minimisation of insurance risks. The main overall goal of reinsurance is to protect the insurance company from considerable claims or a lot of claims and to maintain sufficient capital ratio of insurance companies. The goal is modelling of the insurance process and computer realisation of the algorithm for minimisation of financial risks in insurance.