Portfolio selection under the condition of value preservation

Besides risk and return, investors often are interested in choosing a portfolio such that the portfolio value is preserved. However, the traditional utility-maximizing approach generally fails to provide such a solution. As a different approach value preservation is formulated as an equilibrium problem. Following this approach it is shown that under reasonable assumptions a value preserving solution exists. The solution only depends on the set of feasable portfolio decisions. Contrary to this, the Bernoulli principle in addition requires a utility function that is independent from this set.