source('../Chapter16/utils.R')

a0 = 1.e-3
R0 = 1.05
T = 4

## Car B:
##
c0 = -35
c1 = 12
c2 = 8

p = 0.5

aT = a0 ## since the formula for "a" at time t is at = a0 R^(T-t) and here t=T
vB = c0 + exponential_certainty_equivalent(aT, p, c1, c2)/(R0^T)
print(vB)


## Car A:
##
c0 = -20
c1 = 10
c2 = 5

p = 0.5

## The CE at the upper branch:
##
aT = a0 ## since the formula for "a" at time t is at = a0 R^(T-t) and here t=T
v_upper = (c1 + c0) + exponential_certainty_equivalent(aT, p, c1, c2)/(R0^2)
print(v_upper)
v_lower = (c2 + c0) + exponential_certainty_equivalent(aT, p, c1, c2)/(R0^2)
print(v_lower)

aT = a0*R0^2
vA = c0 + exponential_certainty_equivalent(aT, p, v_upper, v_lower)/(R0^2)
print(vA)