Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
Step 1 – Characterize the Rare Event
A. Location parameter = µ = 1.67
Scale parameter = PV (
T
,) t = 0.88
B. The probability distribution using the Gumbel probability density function is
given by:
−( x−µ
) −( x−µ
)
1
e σ
σ −
f ( x; µσ , ) = e e
Gumbel
σ
1
= e
0.88
−( x−1.67)
0.88
e
−( x−1.67)
0.88
−e
where
x is the random variable of interest (number of hurricanes during the
lifespan of the strategy/policy)
STEP 2 – Calculate Certainty-Equivalent Value of Uncertainty associated with Rare Event
Here, the investment opportunity is to spend $101 million to avoid $100 million in costs per
hurricane event. Equation 4 can be used to derive the certainty equivalent value of uncertainty
associated with the occurrence of hurricanes.
A. Use Equation 4 to calculate the certainty-equivalent value of uncertainty associated with rare
events. Default values for the interest rate and the mean and standard deviation for the process that
generates V are based on those used by Koh and Paxon (2005). Because the Koh and Paxon
formulation embeds the option value into an investment framework, the interest rate is 9% to
reflect a risk premium and inflation.
VALUATION OF TRAVEL-TIME RELIABILITY FOR RARE EVENTS Page C-15