We are concerned with different properties of backward stochastic differential equations and their applications to finance. These equations, first introduced by Pardoux and Peng (1990), are useful for the theory of contingent claim valuation, especially cases with constraints and for the theory...

In a financial market model with constraints on the portfolios, define the price for a claim "C" as the smallest real number "p" such that sup_π E["U"("X"_"T"-super-"x"+"p",&thin sp;π - "C")]≥ sup_π E["U"("X"_"T"-super-"x", π)] , where "U" is the negative exponential utility function and...

Consider an option on a stock whose volatility is unknown and stochastic. An agent assumes this volatility to be a specific function of time and the stock price, knowing that this assumption may result in a misspecification of the volatility. However, if the misspecified volatility dominates the...