Optimal Synthesis in Stochastic Problems with the Control in the Noise and its Applications to Mechanics and Financial Mathematics Problems

Optimal synthesis stochastic problem with the control in the noise are considered. Essential difference of those problems from corresponding deterministic problems is appearing of domain with singular control function. As an applications stochastic problem of correction of movement and a stochastic optimal feedback control problem for a single degree of freedom vibrational system together with stochastic Merton’s investment strategy problem are considered.