Continuous var-criterion and investor's optimal portfolio

The problem of optimal behavior of an investor in the high-developed option market is studied. The investor's risk-preferences function is introduced, and the continuous value at risk-criterion as a continuous generalization of well-known common VaR-criterion is introduced on its basis. Moreover, the investor has his own forecast for probability properties of future behavior of basic option price. The problem is to maximize an average income (or yield) under introduced criterion. The optimal portfolio on the theoretical one-period option market with the given prices picture is constructed. The method is illustrated by an example with two-sided exponential probability distributions.