A stochastic control approach to risk management under restricted information

We use techniques from discrete-time stochastic control under partial state information to determine a shortfall-risk minimizing investment strategy in the case when there is only restricted information on the underlying market model and transaction costs as well as shortselling constraints are present. The approach is adaptive in the sense that it takes into account all the information on the underlying model that becomes successively available to an economic agent by observing the prices in the market. As an immediate byproduct of the approach it is possible to determine the entire shortfall distribution corresponding to the optimal strategy and to various values of the initial capital.