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ACTSC-372-1051-Test1_exam

# ACTSC-372-1051-Test1_exam - E g 23 3 the certainty...

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Unformatted text preview: E g: 23, 3 the certainty equivaleth a} gamblgregrgsent? 11L. Actsc 3?? Test #1‘0 - WENTER 2005 (90 minutes) 5 Questions, 6 marks each Marks: 7 #2. Determine if the feﬁowing statement is TRUE pr FALSE. State your reason. 7 “up” >mAW-Awnvr 7’ > I v a: :1, a ' r 1/“: ‘ a utility functions of the form u(w) ' i ’ ' exhibit decreasing absolute »_-- v ~ ~ risk aversion. «- M l" .. ‘ ‘ .,,..,_‘_,.._A, M . W__,...,,._.g “7., , ., ~ -w. ,4w-_w 3. Suppose that when a decision maker is given the foliewéng ate/e gambﬁes A 3, he ,1 chooses gamble A (Le. he prefers gamble A to gamble B) 5:: A: Winning \$3000 with certainty, or A 1' "f"ff"’“"»’"”B: A 80% chance of Winning \$4000 (and a 20% chance of Winning nothing) The same decision maker is then asked to choose between gambles C and D: 54‘ r * 05% chance Winning\$3000 (and a 75% chance of Wiﬂning nothing), or nee“ {ginning \$4000 (and e 80% chance of Winning nothing) w EEE¥§WGB~makeris then said to have viclated ---/e£\$he-yen»NemgmréMeygensﬁexnaxioms. Explain in detaiis Why. (Notexzhayehere is oﬁéiétencjf“§ii§ée‘E[A] <.E[B} While ’3; < ;_ . ‘ 1f:hé”éhoo\$¢§:gg «5 "7119:. ' 3 "‘ ‘ 'A 7'." :1: “U;- 3ft? .r‘ Justin: 4 4. A decision maker’s ﬁtiiify' fuziction is given by = ~e'0‘003w, 'w > 0. The decisien . maker has an iniiial wealth of we, = 1, OOOandfaces a randomioss X with aipniiarm 7V‘W'"‘m«'faist?i§iiii5ﬁBE».‘ 'What is the maximum premium this decision iéay H for an insurance that pays half of any loss during thé‘n‘ext’périod? List-Q .éity ﬁ.e;_’xiiibited'by iziglgfaverse ingiiyigiual with an exponential utility fuzip‘gigii. : 7 .- 0 5. An individual, with initial weeﬂth level we, is facing a random loss 12v. X that has an , expected loss E(X) = ,u. Suppose H is the minimum (loaded) premium an insurance company IS ‘éﬁéi’giﬁg to completely insure the 1055 X ; 3.9., H=(vl+c)u>+d, c>0,d>0. V I Show that a ris - w’gfsral inﬁjyidual nggtﬂnsurgggémgt 5117923953. ...
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