Abstract: The problems of value-at-risk is an important topic and have already been used widely in the finance market. This paper discusses a new optimal control model of the conditional value-at-risk in the finance market. We present the concept of α-CVaR under the confidence level vector α and its optimal control model (CCVaR) with continuous time, which can be dispersed approximatively to a problem of multi-stages analysis. Then, we present the concept of α-CVaR under the confidence level vector α and its optimal control model (SCVaR) with a discrete case. We prove that the optimal solution to the problem (SCVaR) can be obtained by solving an optimal recursive equation of dynamic programming. It is meaningful to solve the problem of the control model of the conditional value-at-risk.

Key words: optimal control, risk value, loss function, conditional value-at-risk