Mathematical reserves in insurance with equity fund versus a real value of a reference portfolio
Mathematical reserves in insurance with equity fund versus a real value of a reference portfolio

Summary/Abstract: An insurance company, which wishes to secure its solvency, ought to have at its disposal a certain reserved amount referred to in life insurance as a mathematical reserve of premiums. Calculation methods of mathematical reserves in traditional insurance may be found in classical actuarial literature, according to which the reserve is calculated as actuarial value of accumulated future cash flows including death risk and risk of time value of money change, that is, the so-called actuarial risk. However, insurance companies, which offer complex insurance products such as insurance with equity fund (unit-linked insurance), in order to ensure their solvency in accordance with Solvency II, also ought to consider an additional aspect arising from financial risk. Benefits resulting from this type of policy are directly related to implementation of the reference portfolio and thus their stochastic nature ought to be included in valuation. In this article through combining a financial and actuarial approach, the reserves for the unit-linked insurance are determined as an appropriate conditional expected value including extended actuarial risk and the influence of established investment strategy of the insured on their value is investigated.

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