Continuous VaR-criterion in scenario markets

The paper investigates problems of using continuous VaR-criterion (CC-VaR) in scenario market as a discrete analog of ideal theoretical one-period option market. The participation of an investor in the market supposes that the investor prepares a forecast of future underlier’s price distribution and sets the risk-preferences function. A discrete optimization algorithm as the result of projecting the theoretical algorithm based on the Newman–Pearson procedure onto scenario market is suggested. An example of the market with three scenarios, for which the optimality can be broken, is adduced. However, such violations occur seldom and are insignificant. To improve the quality of solutions, randomization of portfolio weights as remedy of smoothing the distribution function is proposed. Special algorithms for calculations connected with yield of randomized portfolios are suggested. The exposition is illustrated by diagrams.