Continuous var-criterion and investor's optimal portfolio

The work investigates the problem of extending the methodology of applying continuous VaR-criterion (CC-VaR) by investors of one-period option markets with one underlier on tasks of constructing the optimal investor’s portfolio for analogical markets with several underliers, i.e., multidimensional markets. The one-period ideal theoretical multidimensional delta-market is defined, and its tools and the algorithm of constructing optimal-on-CC-VaR portfolio of multidimensional delta-instruments by using the Newman – Pearson procedure are formed. In many ways, the algorithm repeats the sequence of operations from the algorithm of the one-dimensional market, but applied to multidimensional objects. The processing of the theoretical algorithm is illustrated by an example of the two-dimensional delta-market, and the optimal solution is searched by analytical methods. The forecast and cost functions, the dissonant, the ordering and weighted functions, and also basic investment performances are calculated. Some singularity presented in the example is eliminated by a natural and rational way and demonstrates possibilities of extending the canonical model. The exposition is illustrated by graphics.