We consider the model where the price of a stock is described by geometric Brownian motions coupled by a finite state Markov chain. The problem is to find an optimal stopping rule – within the class of policies determined by a target price together with a stop-loss limit – which maximizes the expected discounted relative price increase. Using a linear programming approach we numerically determine the optimal threshhold values and compute the corresponding mean holding times and the profit-and-loss probabilities. Read the rest of this entry »
Imagine an investor who owns a stock which he wishes to sell before time T > 0 so as to maximise his profit. The investor has to decide when to sell the stock. Naturally, he would like to sell when the stock price is at its maximal value over the interval [0; T], but such a strategy is impractical since this information is only known at time T. Read the rest of this entry »
Trading in stock markets consists of three major steps: select a stock, purchase a number of shares, and eventuallysell them to make a profit. The timing to buyand sell is extremely crucial. A selling rule can be specified byt wo preselected levels: a target price and a stop-loss limit. This paper is concerned with an optimal selling rule based on the model characterized by a number of geometric Brownian motions coupled bya finite-state Markov chain. Such a policy can be obtained bysolving a set of two-point boundaryv alue differential equations. Read the rest of this entry »
