On stop-loss strategies for stock investments.
This paper deals with the expected return of a stock investment with a stop-loss strategy. For the probability density for the transformed price \(x=\ln s\), \(u(t,x)\) a convection-diffusion equation \[ u_{t}(x,t)={\sigma^2\over 2}u_{xx}(x,t)-\eta u_{x}(x,t) \] with conditions \(u(l(t),t)=0\), \(u(x,0)=\delta(x-x_0)\) is derived, where \(l(t)=\ln(s(t))\), \(s(t)\) is a stock price-per-share, \(\delta(x)\) is a Dirac delta function. The expected value of the investment is evaluated. When the stop-loss criterion is a linear function of time, the exact form for the probability density function is available. Results for two examples with an exact probability density function are presented. The authors design a boundary element method to solve the boundary value problem for a general stop-loss criterion.
scientific article; zbMATH DE number 1860860