Stochastic interest rate in life insurance: The principle of equivalence revisited

Based on financial theory, a valuation model—including stochastic interest rates—for traditional life insurance contracts is derived. The interpretation of the principle of equivalence may be revisited in this framework; single premiums are found as expected present values under a risk adjusted probability measure. Using a specific model of the term structure some new formulas for the market value of various life insurance contracts are derived. A partial differential equation for the market values of the assurances, is deduced, corresponding to the traditional Thiele's differential equation of classical actuarial sciences. This equation contains some interesting new terms.