Optimal trading of an asset in the open market: A dynamic programming approach

Assuming that the asking price of an asset is a random observation from a known distribution function, we first consider the problem of buying an asset and selling it later within a limited period of time. The optimal strategies, derived by means of a stochastic dynamic programming technique, maximize the present value of the expected profit. We then consider the infinite-stage model where there is no time constraint. As a special case of the optimal selling strategy with finite stages, we also propose an option valuation model for the case where the buyer has the right to purchase a certain asset at a specified exercise price within a specified time. The optimal buying and selling strategies derived in the paper can be extended to various directions such as the serially correlated process and the rank-based trading strategy.