Control in binary models with disorder

The paper considers the problem of dynamic control to a portfolio for a binary model with disorder. The a posteriori approach is considered, that is a disorder is detected with the subsequent clustering of the tree nodes in the process of solving the problem. On the basis of this clustering, we construct an algorithm for calculating the optimal dynamic portfolio, which is applicable for binary models with disorder. We use both symmetric and asymmetric penalties for not achieving the set control goal. Further, we analyze the possibility of using a binary model to approximate the Black–Scholes model with disorder, and investigate the possibility of reducing an $NP$-complete problem to $P$-complete problem with loss of information.