Theoretical foundations of continuous VaR criterion optimization in the collection of markets

The work continues studying the problems of using continuous VaR criterion (CC-VaR) in financial markets. The application of CC-VaR in a collection of theoretical markets of different dimensions that are mutually connected by their underliers is concerned. In a typical model of the collection of one two-dimensional market and two one-dimensional markets, the most general case of their conjoint functioning is considered. The rule of constructing a combined portfolio optimal on CC-VaR in these markets is submitted. This rule is founded on misbalance in returns relative between markets with maintaining optimality on CC-VaR. The optimal combined portfolio with three components is constructed from basis instruments of all markets and by using ideas of randomization in their composition. Also, the idealistic and surrogate versions of this combined portfolio, which are useful in testing all algorithmic calculations and in graphic illustrating portfolio's payoff functions, are adduced. The model can be extended without academic difficulties onto markets of greater dimensions. Also, two truncated variants of problem setting with excluded either one of one-dimensional markets or the two-dimensional market are fully justified.