I am not sure if it is self financing and I am wondering if Vt(X) is a martingale

Question 1 Let X be derivative on [0, Tl which is a positive FT measurable random variable. Define VE(X) be the value of X at time t, measured in discounted dollars. A portfolio has bounded risk if there exists N such that for all t, 14(Xk)- N Here is the negative part of V(Xk) and it represents the a.mouut that the portfolio is short on Xk. This basically tells us there is a limit to what we can borrowed. There is no arbitrage with bounded risk if no self-financing portfolio with bounded risk is an arbitrage opportunity. (a) Let; X and Y be derivatives on [0, T] . If X Y a.s., then show that vo(X) vo(Y). Further show that if X = Y ms., then vo(X) = vo(Y). (b) Let l. u 20, 2. o s t ST and 3. X and Y bc derivatives on (O, T] Show that these are all true. (i) vo(0) O, vo(l) 1, and vo(X) 20 vo(X) X 0 me. (iii) vo is linear : vo(X + Y) vo(X) + vo(Y) and vo(aX) -aVo(X) If t > O, vo(X) If A 0 is bounded and F, measurable, then Vt(AX)