In this paper, the approach of BSDE will be employed to study the irreversible investment problem under k-ignorance when the DM is risk- and uncertainty-averse. For the case of logarithmic utility, we work out the explicit solutions of the value of the utilized patent, the value of the...

In this paper, we establish representation theorems for generators of backward stochastic differential equations (BSDEs in short), whose generators are monotonic and convex growth in y and quadratic growth in z. We also obtain a converse comparison theorem for such BSDEs.

We prove the existence and uniqueness of solutions of reflected backward stochastic differential equations in time-dependent adapted and càdlàg convex regions D={Dt;t∈[0,T]}. We also show that the solution may be approximated by solutions of backward equations with reflection in...