EQUITY ALLOCATION AND PORTFOLIO SELECTION IN INSURANCE: A SIMPLIFIED PORTFOLIO MODEL

A quadratic discrete time probabilistic model, for optimal portfolio selection, under risk constraint, is introduced in the context of (re-) insurance and finance. The portfolio is composed of contracts with arbitrary underwriting and maturity times. For positive values of underwriting levels, the expected value of the accumulated final result is optimized under constraints on its variance and on annual Returns On Equity. Existence of a unique solution is proved and a Lagrangian formalism is given. An effective method for solving the Euler-Lagrange equations is developed. The approximate determination of the multipliers is discussed. This basic model, which can include both assets and liabilities, is an important building block for more general models, with constraints also on non-solvency probabilities, market-shares, short-fall distributions and Values at Risk.