Value at Risk (VaR) is used to illustrate the maximum potential loss under a given confidence level, and is just a single indicator to evaluate risk ignoring any information about income. The present paper will generalize one-dimensional VaR to two-dimensional VaR with income-risk double...

The present paper considers a class of financial market with transaction costs and constructs a geometric no-arbitrage analysis frame. Then, this paper arrives at the fact that this financial market is of no-arbitrage if and only if the curvature 2-form of a specific connection is zero....