In that paper, we solve dynamically a partial hedging problem for an American contingent claim: assuming superhedging is not feasible, we explain in this context the notion of efficient hedging by introducing a risk minimization criterion: we consider here the problem of minimizing the conditional expected loss for a given convex and non decreasing loss function. To solve this problem, we provide a connection between the dynamic convex risk functional introduced and the solutionof a quadratic RBSDE (Reflected Backward Stochastic Differential Equations): this is achieved by studying the properties of specific non linear expectations  .
In that paper, we provide a new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver g is convex and has quadratic growth in its second variable: this is done by introducing the extended notion of g-Snell enveloppe. Then, in a second step, we relate this representation to a specific class of dynamic monetary concave functionals already introduced in a discrete time setting. This connection implies that the solution, characterized by means of non linear expectations , has again the time consistency property .
D
solve dynamically a partial hedging problem for an American contingent claim: assuming superhedging is not feasible, we explain in this context the notion of efficient hedging by introducing a risk minimization criterion: we consider here the problem of minimizing the conditional expected loss for a given convex and non decreasing loss function. To solve this problem, we
R
connection between the dynamic convex risk functional introduced and the solutionof a quadratic RBSDE (Reflected Backward Stochastic Differential Equations): this is achieved by studying the properties of specific
new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver g is convex and has quadratic growth in its second variable: this is done by introducing the extended notion of g-Snell enveloppe. Then, in a second step, we relate this representation to a specific class of dynamic monetary concave functionals already introduced in a discrete time setting. This connection implies that the solution, characterized by means of
A
, has again the time consistency property