For a standard Black-Scholes type security market, completeness is equivalent to the solvability of a linear backward stochastic differential equation (BSDE). An ideal case is that the interest rate is bounded, there exists a bounded risk premium process, and the volatility matrix has certain surjectivity. In this case the corresponding BSDE has bounded coefficients and it is solvable leading to the completeness of the market. However, in general, the risk premium process and/or the interest rate could be unbounded. Then the corresponding BSDE will have unbounded coefficients. For this case, do we still have completeness of the market? In order to answer this question, the author defines so called exponential process and provides various estimates for this process, under various integrability conditions on its parameters. In the case that the coefficients are not necessarily bounded, some sufficient conditions are presented under which the BSDEs are solvable which leads to the completeness of the corresponding markets. It is important to note that the spaces of the portfolios and the contingent claims are allowed to have different integrability. Two illustrative examples are presented.