Conditions for optimality in the infinite-horizon portfolio-cum-saving problem with semimartingale investments

A model of optimal accumulation of capital and portfolio choice over an infinite horizon in continuous time is formulated in which the vector process representing returns to investments isa general semimartingale. Methods of stochastic calculus and calculus of variations are used to obtain necessary and sufficient conditions for optimality involving martingale properties ofthe shadow price processes associated with alternative portfolio cum saving plans.The relationship between such conditions and portfolio equations is investigated.The results are appliedtospecial cases where the returns process has stationary independent increments and the utility function has the discounted relative risk aversion form