Equilibrium in a stochastic model with consumption, wages and investment

Existence of equilibrium is established in a continuous time economy where a finite number of agents derive utility from consuming both good and leisure. They own and trade shares of the means of production of the good as well as financial assets. Share prices are modeled as Itô processes. The agents derive income from dividends paid out to shareholders of the productive asset and from wages. They choose a consumption policy, a leisure policy, and an investment strategy which maximizes their utility. The manager of the production facility chooses employment rates so as to maximize profit. Labor is transformed into goods through a production function. The only exogenous quantities are the parameters of the financial market. Two simple examples are solved explicitly.