Please help with the following question - BEHAVIORAL FINANCE:

QUESTION 1: DECISION UNDER RISK QUESTION 1 - PART 1: Assume that Norman, who follows Rank-dependent utility maximization as described above, has on his best day rational expectations. In the context of of Rank-dependent wutility maximizer this means that Norman uses the objective probabilities described previously as an input to weight probabilities and make choices. Noman can choose among the following options: 1) Invest in Stock A, 2) invest in Stock B, or 3) not invest at all Norman maximizes expected happiness. He is a rich person with a wealth of W=5,000,000 DKK, with utility function (2) = ln(2) and is deciding how to invest his portfolio. Norman is a Rank-dependent utility maximizer with a probability weighting function given by w(p) = p01. If a given stock costs and pays either X or Y, with X greater than Y, with objective probability p and 1-A, respectively, then Norman maximizes the following Rank-dependent utility valuation: RDU = w[p) + u(W + x C) + (1 w(p))(W + Y C) Norman can choose from two different stocks, stock A or stock B. Each Stock A costs 500, and each A stock pays out either 600 or 200 DKK per stock, with 70% and 30% probability, respectively. Stock B also is priced at 500 per share but yields either 1500 or 100 DKK per stock with 10% and 90% probability, respectively. These probabilities represent the actual objective probability distributions of retums of each stock. Therefore, someone with rational expectations should use such probabilities when deciding whether or not to buy the stocks. Norman will invest all his wealth in either Stock A or in Stock B, or in just cash. This means that he will buy 10,000 shares of either Stock A or Stock B if he decides to invest at all. For example, if he buys Stock A and the good outcome realized, Norman will receive 10,000*600 = 6,000,000 DKK. This question is divided in 2 parts. Which of the three options will Norman choose as his best option Furthermore, notice that both stocks have negative expected returns. How is it possible that Noman decides to have one of the stocks? (Hint: If Norman didn't weight probabilities (.e., w(p) = p), be would doase not to invest at all. Calculate and compare the utility of not investing in the stock market, the Rask-dependent Mility of inesting in Stock A, the Rank-depende nat tility of intesting in Stock B QUESTION 1 - PART 2 Now, suppose that Norman has been checking the financial news lately, and he has become convinced that all signs indicate that there could be an economic/financial recession coming and he becomes financially" scared. When Norman feels this scare, his reaction is to become pessimistic towards probabilities, and his probability weighting function changes to w(p) = p.25. Re-evaluate Norman's choices in part 1 of this question. Does he invest in Stock A? In Stock B? Or not invest at all? If there is a change in investment preferences, how can you intuitively explain the nature of this change? QUESTION 1: DECISION UNDER RISK QUESTION 1 - PART 1: Assume that Norman, who follows Rank-dependent utility maximization as described above, has on his best day rational expectations. In the context of of Rank-dependent wutility maximizer this means that Norman uses the objective probabilities described previously as an input to weight probabilities and make choices. Noman can choose among the following options: 1) Invest in Stock A, 2) invest in Stock B, or 3) not invest at all Norman maximizes expected happiness. He is a rich person with a wealth of W=5,000,000 DKK, with utility function (2) = ln(2) and is deciding how to invest his portfolio. Norman is a Rank-dependent utility maximizer with a probability weighting function given by w(p) = p01. If a given stock costs and pays either X or Y, with X greater than Y, with objective probability p and 1-A, respectively, then Norman maximizes the following Rank-dependent utility valuation: RDU = w[p) + u(W + x C) + (1 w(p))(W + Y C) Norman can choose from two different stocks, stock A or stock B. Each Stock A costs 500, and each A stock pays out either 600 or 200 DKK per stock, with 70% and 30% probability, respectively. Stock B also is priced at 500 per share but yields either 1500 or 100 DKK per stock with 10% and 90% probability, respectively. These probabilities represent the actual objective probability distributions of retums of each stock. Therefore, someone with rational expectations should use such probabilities when deciding whether or not to buy the stocks. Norman will invest all his wealth in either Stock A or in Stock B, or in just cash. This means that he will buy 10,000 shares of either Stock A or Stock B if he decides to invest at all. For example, if he buys Stock A and the good outcome realized, Norman will receive 10,000*600 = 6,000,000 DKK. This question is divided in 2 parts. Which of the three options will Norman choose as his best option Furthermore, notice that both stocks have negative expected returns. How is it possible that Noman decides to have one of the stocks? (Hint: If Norman didn't weight probabilities (.e., w(p) = p), be would doase not to invest at all. Calculate and compare the utility of not investing in the stock market, the Rask-dependent Mility of inesting in Stock A, the Rank-depende nat tility of intesting in Stock B QUESTION 1 - PART 2 Now, suppose that Norman has been checking the financial news lately, and he has become convinced that all signs indicate that there could be an economic/financial recession coming and he becomes financially" scared. When Norman feels this scare, his reaction is to become pessimistic towards probabilities, and his probability weighting function changes to w(p) = p.25. Re-evaluate Norman's choices in part 1 of this question. Does he invest in Stock A? In Stock B? Or not invest at all? If there is a change in investment preferences, how can you intuitively explain the nature of this change