Functional Limit Theorems For Stochastic Integrals With Applications To Risk Processes And To Self-Financing Strategies In A Multidimensional Market

We study sufficient conditions for the weak convergence of stochastic integrals with respect to processes of bounded variation, martingales, or semimartingales. A semimartingale theorem is extended to the multidimensional case. We apply a limit procedure and pass from processes of bounded variation to risk processes. An “inverse” problem for the weak convergence is also considered.