The stochastic control method is one of the stochastic methods that deals with dynamic systems subject to uncertainty. In portfolio optimization, the objective of stochastic control methods is to find the optimal investment strategy that maximizes expected returns or achieves other objectives, taking into account the risk associated with uncertain market conditions. Stochastic control methods, on the other hand, explicitly incorporate the stochastic nature of asset returns and are designed to find strategies that are resilient to market fluctuations. A non-linear partial differential equation called the Hamilton-Jacobi-Bellman (HJB) equation is used to define necessary and sufficient conditions for the optimality of the control with respect to the loss function. In general, it is computationally intractable and the existence and uniqueness of the solution are non-trivial. In order to compute an explicit solution, assumptions are needed in the process. One of the major assumptions to be able to obtain an explicit solution is the assumption of constant market coefficients. If we want to predict the portfolio weights and thus the return on our investments in real time, we also need to take the real market coefficients, which change on a daily basis, so this assumption is much too strict. When comparing the stochastic control method and the use of more modern techniques, such as machine learning, for a simple example of a portfolio of 5 stocks, the modern technique proves superior.
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