3. Suppose you are on the quant team at a stock market firm. Suppose the brokerage team is advising a client on whether to invest in stock X or stock Y. Suppose the quant team derived each stock's time series equation, shown below. Given this, answer the client's questions. Stock X: Let Xt denote the share price of stock X at time t, where the initial purchase price per share of stock X is one dollar; that is, Xo = 1. Suppose the quant teams analysis of this stocks price per share over t results in the time series model given by 10xt-1 xt = 1+x{1 where t > 1 and t is a positive integer (e.g., t= day 1, day 2, day 3, ...). Stock Y: Let Yt denote the share price of stock Y at time t, where the initial purchase price per share of stock Y is one dollar; that is, yo = 1. Suppose the quant team's analysis of this stocks price per share over t results in the time series model given by 1097-1 Yt = 1 + yt-1 1. Do either of these stocks show oscillatory behavior in their price per share over time? If so, characterize the oscillatory behavior as finite or infinite? 2. Apply Brouwer's theorem to find the price per share fixed points of each stock. Prove whether each stock exhibits price per share stability over time? If stability exists, then what price per share does that stock converge to and from what point in time t does that behavior continue? 3. Over time, which stock provides the best return above the initial purchase price and why? 3. Suppose you are on the quant team at a stock market firm. Suppose the brokerage team is advising a client on whether to invest in stock X or stock Y. Suppose the quant team derived each stock's time series equation, shown below. Given this, answer the client's questions. Stock X: Let Xt denote the share price of stock X at time t, where the initial purchase price per share of stock X is one dollar; that is, Xo = 1. Suppose the quant teams analysis of this stocks price per share over t results in the time series model given by 10xt-1 xt = 1+x{1 where t > 1 and t is a positive integer (e.g., t= day 1, day 2, day 3, ...). Stock Y: Let Yt denote the share price of stock Y at time t, where the initial purchase price per share of stock Y is one dollar; that is, yo = 1. Suppose the quant team's analysis of this stocks price per share over t results in the time series model given by 1097-1 Yt = 1 + yt-1 1. Do either of these stocks show oscillatory behavior in their price per share over time? If so, characterize the oscillatory behavior as finite or infinite? 2. Apply Brouwer's theorem to find the price per share fixed points of each stock. Prove whether each stock exhibits price per share stability over time? If stability exists, then what price per share does that stock converge to and from what point in time t does that behavior continue? 3. Over time, which stock provides the best return above the initial purchase price and why
