PDE Question:
Assume for example that a broker
buys a stock at a certain price m. She decides in advance to sell it if its price reaches an upper bound m2 (in order to cash in her profit) or a lower bound m1 (to minimize losses in case the stock dives). How much time on average will the broker hold the stock, assuming that the stock price performs a Brownian motion? This is a one-dimensional version of the model we derived. The equation and the associated boundary conditions are:

Question

PDE Question: 
Assume for example that a broker
buys a stock at a certain price m. She decides in advance to sell it if its price reaches an upper bound m2 (in order to cash in her profit) or a lower bound m1 (to minimize losses in case the stock dives). How much time on average will the broker hold the stock, assuming that the stock price performs a Brownian motion? This is a one-dimensional version of the model we derived. The equation and the associated boundary conditions are:

anonymous · Answer

$$k*u''(m) = -1, u(m_1)=u(m_2)=0$$