270 Index N nodal set, 53 nodal solution, 90 nonsolvable, 10,139 O option, 7 call, 7 optimal control, 53 optimal control problem, 3,52 optimality system, 4 ordinally equivalent, 6 P parabolicity, 104 degenerate, 104 super, 104 portfolio, 7 price exercise, 7 fair, 8 problem, optimal control, 3,52 Skorohod, 169 R rate appreciation, 7,208 interest, 7 recursive utlity, 5 reflected BSDE, 171 FBSDE, 181 FSDE, 169 risk -neutral, 227 premium, 8,227 S semi-concave, 61 solution adapted, 10,25,138 approximate, 54 nodal, 90 viscosity, 66 sub-, 66 super-, 66 solvable, 10,139 approximately, 54 stock, 7 subdifferential, 174 T target, 52 Theorem comparison, 22,214 martingale representation, 2 U utility current, 5 process, 5 recursive, 5 V value function, 58 lower, 233 upper, 233 viscosity solution, 66 subsolution, 66 supersolution, 66 volatility, 7,208 W weight vector, 6 Y Yosida approximation, 174 . nodal, 90 viscosity, 66 sub-, 66 super-, 66 solvable, 10,139 approximately, 54 stock, 7 subdifferential, 174 T target, 52 Theorem comparison, 22,214 martingale representation, 2 U utility