Completeness of security markets and backward stochastic differential equations with unbounded coefficients
Abbreviated Journal Title
Nonlinear Anal.-Theory Methods Appl.
Completeness; Backward stochastic differential equations; Exponential; super-martingale; Mathematics, Applied; Mathematics
For a standard Black-Scholes-type security market, completeness is equivalent to the solvability of a linear backward stochastic differential equation (BSDE). When the interest rate is bounded, there exists a bounded risk premium process, and the volatility matrix has certain surjectivity, then the BSDE will be solvable and the market will be complete. However, if the risk premium process and/or the interest rate is not bounded, one gets a BSDE with unbounded coefficients to solve. In this paper, we will discuss such a situation and will present some solvability results for the BSDE which will lead to the completeness of the market. (C) 2005 Elsevier Ltd. All rights reserved.
Nonlinear Analysis-Theory Methods & Applications
"Completeness of security markets and backward stochastic differential equations with unbounded coefficients" (2005). Faculty Bibliography 2000s. 5811.