We consider the process
{
x
−
N
(
t
)
:
t
≥
0
}
\{x-N(t):t\geq 0\}
, where
x
∈
R
+
x\in \mathbb {R}_+
and
{
N
(
t
)
:
t
≥
0
}
\{N(t):t\geq 0\}
is a renewal process with light-tailed distributed holding times. We are interested in the joint distribution of
(
τ
(
x
)
,
A
(
x
)
)
(\tau (x),A(x))
where
τ
(
x
)
\tau (x)
is the first-passage time of
{
x
−
N
(
t
)
:
t
≥
0
}
\{x-N(t):t\geq 0\}
to reach zero or a negative value, and
A
(
x
)
≔
∫
0
τ
(
x
)
(
x
−
N
(
t
)
)
d
t
A(x)≔\int _0^{\tau (x)}(x-N(t))dt
is the corresponding first-passage (positive) area swept out by the process
{
x
−
N
(
t
)
:
t
≥
0
}
\{x-N(t):t\geq 0\}
. We remark that we can define the sequence
{
(
τ
(
n
)
,
A
(
n
)
)
:
n
≥
1
}
\{(\tau (n),A(n)):n\geq 1\}
by referring to the concept of integrated random walk. Our aim is to prove asymptotic results as
x
→
∞
x\to \infty
in the fashion of large (and moderate) deviations.