Continous time optimal stochastic growth: local martingales, transversality and existence

Publication Date
Financial Markets Group Discussion Papers DP 479
Publication Authors

The present work deals with optimal planning in continuous time, infinite horizon, stochastic neo-classical one-sector models of economic growth (or decline). In the main model, called the Standard Model, the influence of risk is represented in an abstract way by the measurability of production and utility with respect to a general filtration, while the equation of accumulation is written as a random ordinary differential equation. We also consider a model in which depreciation, technological progress, population and impatience are modelled as general semimartingales and the equation of accumulation may be written as a stochastic differential equation, and show that this can be represented as a special case of the Standard Model.