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Student SID (PK) sname saddress GPA Program DID (PK) pname faculty Undergraduate SID (FK to Student) |pID (FK to Program) year Graduate sID (FK to Student) pID (FK to Program) thesis year Course CID (PK) PID (FK to Program) cname TA SID (FK to Student) CID (FK to Course) Room Enrolled SID (FK to Student) CID (FK to Course) Grade Write a SQL query for each of the following questions: E) Find the TA's name and room for the course named 'Databases'. Please make sure you copy your answers from Relax, (https://dbis- uibk.github.io/relax/landing)This is Actuarial Science 9'. Sam purchased a stock that pays dividends of EDI] at the end of the first year and increases by SUI each yearthereafter. At an annual effective interest rate of i: the price of this stock is 46,3513. Calculate i. 3*". Consider a share of stock that pays annual dividends as follows: 2GB, Ell'l'], E'il}, 2UD[L09]\"2, , Z.'9]\"12 at times CI, 1, 2, , 12 and level payments of EDUQPlE afterward at times 13, 14, Find the purchase price of this share of stock at an annual effective rate of interest i = 4%. 5. A stock pays a dividend of SBDCI at the end of the Fth year {at time 1"}, with each subsequent annual dividend being k'h': greater than the preceding one. Find lt ifthe price of this stock is 33221.52 at an annual effective yield rate of 3%. Hint: The dividend discount model gives the price of the stock one year before the first dividend. ice Problems for the fir Banner Bb Comprehensive Assignment Be Practice Problems for th X G https://mybb.qu.edu.qa/bbeswebdav/pid-2330492-dt-content-rid-6948640_1/courses/Spring_2020_MATH222_21418/Practice%20Problems%20for% # - + 0 Fit to page Page view A" Read aloud . Add not 20. Let f(x) = - and g(x) = if : >0 1+1 ifx va, and define In+1 = 5 (In + " ). Show that (En ) decreases monotonically, bounded and lim En = Va.It had been a quiet Monday morning for Anna Hogue, senior project manager at Flagstone Consulting. Everything seemed to be falling into place forthe company's first conference, 'Healthcare Management in the New Millenium,' scheduled for October 11 and 12 in Eloston. Then Ethan Tang, the staff consultant in charge of registration, stuck his head in the door. \"Anna,\" said Ethan, 'I think we may have a problem with the conference. Only 15 people have registered. |Blur marketing consultants told us to expect at least a 3% registration rate from our direct mail campaign. Based on the 5,060 conference fliers we mailed, do you think another 135 people will register in the next three weeks?\" Anna and Ethan had worked together to develop a budget for the conference, as follows. Them.r had budgeted for registration response rates of 2%, 3%, and 4%, but a response rate of I3.33% was far outside their expectations. 1. a) Employing first and second derivatives of the following utility functions, classify them as either risk- averse, risk neutral or risk-seeking: 1. i) u(x) = In(x) 2. ii) u(x) = x*2 3. iii) u(x) = 2x b) Explain the difference between 'loss-aversion' and 'risk aversion' while defining suitable measures for both. 2. c) Abraham has preferences represented by the utility function u(w) = In(w) while Sarah has preferences represented by the utility function v(w)=a(u(w))+b. Sarah and Abraham are both willing to invest $1,000 in risky investments when their wealth is f10,000 each. With suitable computations, state how much Abraham and Sarah will each be willing to invest in risky assets when their wealth increases to $20,000 each. Explain. 3. d) State the conditions necessary to ensure that when deciding between risky investments, the choices made under the expected utility approach are consistent with choices made in the mean-variance approach.Consider a risk-averse individual with a utility of wealth function U(w) = w^1/3 and initial wealth w = $500 faced with a risky investment. The asset provides a guaranteed return / = 10% with a potential capital gain of 60% of the asset's value and a potential capital loss of 30% of the asset's value.The value of the asset B is$100. 1. Calculate the wealth in the good state wG (capital gain), the wealth in the bad state wl (capital loss), and the expected gamble EG 2. Given the individual's risk-averse utility function, calculate the first and second derivatives: U'(w) and U" (w). Are these derivative calculation results consistent with the theory of risk-averse individuals? Why? 3. Calculate the utility from the good state U(WG), utility from the bad state U(WL), the utility of the expected gamble U(EG), and the expected utility of the gamble EU(G)Uncertainty & Gamble Consider a risk-averse individual with a utility of wealth function U(w) = wos and initial wealth w = $500. He can invest all his wealth in a safe asset. The asset provides a guaranteed return r = 10% . He can also invest all his wealth in a risky Gamble with a potential capital gain of 60% of the asset's value and a potential capital loss of 30%% of the asset's value. The probability of a capital gain is 65% and the probability of a capital loss is 35%. 1. Calculate the wealth in good state we and bad state w, for the risky gamble and the expected wealth from this gamble (EG) and compare this with the Expected wealth from safe investment 2. Given the individual's utility function, calculate the second derivative: U"(w). What does the value of the derivative for positive values of W tell you about the risk preference of this individual? 3. For the risky gamble, calculate utility in the good state U(Wc), utility in the bad state U(W,), the utility of expected wealth of the gamble U(EG), and the expected utility from playing the gamble EU (G) 4. From the expected utility of the gamble, calculate the certainty equivalence CE of the gamble. 5. Using the certainty equivalence CE and expected gamble wealth EG, calculate the risk premium RP of the gamble for this individual. What does this risk premium tell you about this individual? (Risk Premium = EG - CE) 6. Sketch an appropriately labeled utility of wealth diagram with all the components of the gamble: utility of wealth function, wealth in the good/bad states, expected wealth from gamble, utility of wealth in the good/bad states, utility from expected wealth of gamble U(EG), and expected utility of the gamble E(U(G)). 7. From the first and second derivatives of U, find the coefficient of absolute risk aversion (CARA), and coefficient of relative risk aversion (CRRA): Ra(w) = - Ur(w) UM(W R.(w) = Ra(w) xw Your answers will be in terms of w 8. Are your results from the CARA and CRRA calculations consistent with the Arrow/Pratt theory of risk averse behavior? Why?1. Consider the simple regression model: Vi = Bo+ Biri + Hi, for i = 1, ... . n, with E(uilz,) - 0 and let a be a dummy instrumental variable for I, such that we can write: Ci =not matu with E(uilz;) = 0 and E(viz) =0. (c) Denote by no, the number of observations for which = = 0 and by n, the number of observations for which a, = 1. Show that: (a - 2) = =(n-m). 1=1 and that: [( - =)(y: - 9) = -(n - n) (31 - 30) . where to and g are the sample means of y for z equal to 0 and 1 respectively. ( Hint: Use the fact that n = nj + no, and that = = m). (d) Now we regress y on i to obtain an estimator of &. From the standard formula of the slope estimator for an OLS regression and using the result in (c), show that: B - 91 -90 $1 - To This estimator is called the Wald estimator