Graphics Reference
In-Depth Information
Figure
.
.
“Probability gates” are an interactive graphical tool used for determining the probability
thattheprocesspassesthroughaspecifiedinterval.he
.
,...,
.
-quantilelines(thick lines)arebased
on
simulated trajectories (thin lines) of the risk process originating at u
billion USD. he
parameters of the α-stable Lévy motion approximation of the risk process were chosen to comply with
PCS data. From the SDE-Solver
=
Probability Gates
6.4.4
“Probabilitygates”areaninteractivegraphicaltoolimplementedinSDE-Solver.hey
can provide invaluable assistance in the real-time analysis of the risk process and
its models. A “probability gate” gives the so-called cylindrical probability P
X
t
(
at
aspecifiedpointintimet
(Janicki and Izydorczyk,
; Janicki et al.,
). Two
probability gates are defined in Fig.
.
; Monte Carlo simulations can be used to ob-
tain the probability estimates. One yields the probability of the risk process falling
below
billion ater four years, i.e., P
a, b
]
that the simulated process X
t
passes through a specified interval
(
a, b
]
R
(
,
] =
.
. he other yields the
probability of the risk process being in the range
(
,
]
billion ater eight years,
i.e., P
.
. Additionally, product probabilities of the process
passingthroughall ofthe definedgatesareprovided.Intheabove example, theprod-
uct probability of the risk process first falling below
billion (ater four years) and
then recovering toover
billion but lessthan
billion (atereight years) is equal
to P
R
(
,
] =
.
. he parameters of the α-stable Lévy
motion approximation (Furrer et al.,
)of the risk processwere chosen tocomply
with the catastrophic data example.
R
(
,
]
, R
(
,
] =
