Optimum portfolio diversification in a general continuous-time model

The problem of determining optimal portfolio rules is considered. Prices are allowed to be stochastic processes of a fairly general nature, expressible as stochastic integrals with respect to semimartingales. The set of stochastic differential equations assumed to describe the price behaviour still allows us to handle both the associated control problems and those of statistical inference. The greater generality this approach offers compared to earlier treatments allows for a more realistic fit to real price data. with the obvious implications this has for the applicability of the theory. The additional problem of including consumption is also considered in some generality. The associated Bellman equation has been solved in certain particular situations for illustration. Problems with possible reserve funds, borrowing and shortselling might be handled in the present framework. The problem of statistical inference concerning the parameters in the semimartingale price processes will be treated elsewhere.