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Optimal Consumption Until Ruin for an Endowment Described by an Autonomous ODE for an Infinite Time Horizon
Ist Teil von
Mathematics of operations research, 2016-08, Vol.41 (3), p.953-968
Ort / Verlag
Linthicum: INFORMS
Erscheinungsjahr
2016
Link zum Volltext
Quelle
Business Source Ultimate
Beschreibungen/Notizen
We give an algorithmic solution of the optimal consumption problem
sup
c
∫
[
0
,
τ
]
e
−
β
t
d
C
t
, where
C
t
denotes the accumulated consumption until time
t
, and τ denotes the time of ruin. Moreover, the endowment process
X
t
is modeled by
X
t
=
x
+
∫
0
t
μ
(
X
s
)
d
s
−
C
t
. We solve the problem by showing that the function provided by the algorithm solves the Hamilton-Jacobi (HJ) equation in a viscosity sense and that the same is true for the value function of the problem. The argument is finished by a uniqueness result. It turns out that one has to change the optimal strategy at a sequence of endowment values, described by a free boundary value problem.
Finally we give an illustrative example.