QuoteOriginally posted by: DoubleTroubleThank you for your hints bwarren, that was about all the help I needed! I feel really stupid for not figuring out (2)! I just have one question regarding (1). Is it a reasonable restriction to assume that the Stock is modeled by a GBM with constant rate of return and constant volatility like GuitarTrader does? If we assume this, then this is how I reason:The map is obviously convex so we can use Jensen's inequality in the following way:sinceThe only question mark I have is the fact that we assume the stock price to have constant rate of return and volatility. Any comments on this? Is it possible to do in another way without assuming this?Thanks in advance!I was able to show it using Jensen's inequality just assuming the drift of the stock is >= r, i.e. the market price of risk is nonnegative. I think this is reasonable since a rational person would not invest in a risky asset with a negative excess return.