Solutions Manual for Financial Markets Theory: Equilibrium, Efficiency and Information (Springer Finance) by Emilio Barucci & Claudio Fontana – Step-by-Step Exercise Solutions

SOLUTIONS MANUAL

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Financial Markets Theory Equilibrium, Efficiency and Information
2ND Ed Solutions Manual


Exercises of Chapter 2


Solution of Exercise 2.2:
(i) : It suffices to apply De l’Hoˆpital’s theorem:

1 b— 1
lim (a + bx) b — 1
b→1 b — 1
= lim(a + bx)b—1b 1 log(a + bx) + x(b — 1)
b→1 b2 b(a + bx)
= log(a + x).

(ii) : It suffices to note that:
b— 1
1 bx b x —n x
lim 1+ = — lim 1 + = —e— a .
b→0 b — 1 a n→∞ an

(iii) : It suffices to apply De l’Hoˆpital’s theorem:
1 — eax lim xeax x
lim =— =— .
a→0 a a→0



Solution of Exercise 2.4:
Due to condition (2.4), the risk premium ρu(x˜) solves the following equation:
b 2 b
µ — ρu(x˜) — µ — ρu(x˜) = u E[x˜] — ρu(x˜) = E u(x˜) = µ — σ 2 + µ 2 .
2 2
The above condition amounts to the following second order equation for ρu(x˜):
b 2 b 2
— ρu(x˜) + (µb — 1)ρu(x˜) + σ = 0.
2 2
Under the condition that µ < 1/b, the positive root is given by
r
2
1— 1+ b
µb—1 σ2
ρ u(x˜) = .
b/(µb — 1)


Solution of Exercise 2.5:
Due to condition (2.4), the risk premium ρu(x˜) solves the following equation:
1 1 a
— exp —a µ — ρu(x˜) = u E[x˜] — ρu(x˜) = E u(x˜) = — exp —a µ — σ 2
a a 2