Time change in modelling, stochastic calculus and control
Time change is a powerful technique for generating noises and providing flexible models. Its main idea stands in the representation of complicated stochastic structures by some known processes and a randomly perturbed time line. We shall provide an excursus through related stochastic calculus, chaos structure and information, integral representations and stochastic differentiation. These will then be applied to backward stochastic differential equations and optimal control problems. Motivation of our work is taken from stochastic finance.