SITI Compte the arbitrage price, ..), of this claim, at time for the current of the stock Consider both the use when IT and whes To Question (35 points) We comider the portfolio optimistion problem sein das made 12) and incorporate into the model acosomption procesa C)where20dmete respectively the amount ced at time on. He salir and random We call an investment consaption strategy apat (C), wheel (HHN) the tring state detined in c. Next, we note the stable at time to An investment comption plan is mid to be able = what (demote in the color outsimestel ottime and spectively The quantity = 1.8.(0) the invested at time. We can again solve this problem with standard optimization theory of the martingale approach. We choose the 1. (points) Suppose the comption process fired show that there is a trading strategy Il such that (1) ene if And only if for every tiskutoleobability mesure Next, we write the optimizati problem ON sabject to + H+H.S.(0) - , , - ,8,10 - 204 2011 Using the martingapproach, we break the problem down into two The first step in solving the problem max.) mbject to +/- The second step will counist in determining the trading strategy that sprietates the atingetit 25 points) Write the objective fiction with a Lagrange multiple 1 points) Write the first-onder optimality condition 4 pointe Deloretical expedies for c) in ms of the infletion of the derivative of the utility function pot)se the cost to ce a conditions 6.5 points) Finally, we the exponential utilityfition-expl) and that B-1 + Wer is constant Substitute this partitility funtion bank not into the solution computed in 54-5 7. (5 posts) Write the worstem of equation that to be solved in the second step toe that you cannot solve it without specifying further the model) SITI Compte the arbitrage price, ..), of this claim, at time for the current of the stock Consider both the use when IT and whes To Question (35 points) We comider the portfolio optimistion problem sein das made 12) and incorporate into the model acosomption procesa C)where20dmete respectively the amount ced at time on. He salir and random We call an investment consaption strategy apat (C), wheel (HHN) the tring state detined in c. Next, we note the stable at time to An investment comption plan is mid to be able = what (demote in the color outsimestel ottime and spectively The quantity = 1.8.(0) the invested at time. We can again solve this problem with standard optimization theory of the martingale approach. We choose the 1. (points) Suppose the comption process fired show that there is a trading strategy Il such that (1) ene if And only if for every tiskutoleobability mesure Next, we write the optimizati problem ON sabject to + H+H.S.(0) - , , - ,8,10 - 204 2011 Using the martingapproach, we break the problem down into two The first step in solving the problem max.) mbject to +/- The second step will counist in determining the trading strategy that sprietates the atingetit 25 points) Write the objective fiction with a Lagrange multiple 1 points) Write the first-onder optimality condition 4 pointe Deloretical expedies for c) in ms of the infletion of the derivative of the utility function pot)se the cost to ce a conditions 6.5 points) Finally, we the exponential utilityfition-expl) and that B-1 + Wer is constant Substitute this partitility funtion bank not into the solution computed in 54-5 7. (5 posts) Write the worstem of equation that to be solved in the second step toe that you cannot solve it without specifying further the model)
