Multiplicative approximation of wealth processes involving no-short-sales strategies via simple trading (Q2847245)

In financial terms, stochastic integration using general predictable integrands means that continuous trading in the market is allowed. However, in reality, agents in the market can only use simple finite combinations of buy-and-hold strategies. Taking this into account, the paper deals with the following question: can wealth processes that are obtained by allowing continuous trading be closely approximated via simple buy-and-hold trading? If the answer to the previous question is affirmative, how can this eventually be achieved? The contribution of the paper is an approximation result for wealth processes involving no-short-sales strategies allowing only simple wealth processes. The approximation is based on controlling the proportions of wealth invested in the assets. An intermediate result is established that provides multiplicative-type approximation of positive stochastic integrals. An application of the main approximation result to the expected utility maximization problem is also described.