On stop-loss strategies for stock investments

This paper studies the expected return of a stock investment with a stop-loss strategy. The probability density function (p.d.f.) for the investment value is formulated as the solution for a boundary value problem of a partial differential equation. Then, the expected value is manipulated as a function of the stop-loss probability. Two examples are solved by an analytic method. Finally, we design a boundary element method to solve the boundary value problem for a general stop-loss criterion.