Before revision:  marked point processes and in presence of margin requirements such as different interest rates for borrowing and lending and risk premiums for short positions . Margin requirements are modelled by adding in a margin payment function to the investor's wealth equation which is nonlinear with respect to the portfolio proportion process .
After revision:  marked point processes and so-called non-linear wealth dynamics which allows to take account of relaxed assumptions such as differential borrowing and lending and risk premiums for short positions . Margin requirements are modelled by adding in a margin payment function to the investor's wealth equation which is nonlinear with respect to the portfolio proportion process .