We consider the classical optimal dividend payments problem under the Cram\'er-Lundberg model with exponential claim sizes subject to a constraint on the time of ruin (P1). We use the Lagrangian dual function which leads to an auxiliary problem (P2). For this problem, given a multiplier \Lambda, we prove the uniqueness of the optimal barrier strategy and we also obtain its value function. Finally, we prove that the optimal value function of (P1) is obtained as the point-wise infimum over \Lambda of all value functions of problems (P2) . We also present a series of numerical examples.
We consider the classical optimal dividends problem under the Cram\'er-Lundberg model with exponential claim sizes subject to a constraint on the time of ruin . We introduce the dual problem and show that the complementary slackness conditions are satisfied, thus there is no duality gap. Therefore the optimal value function can be obtained as the point-wise infimum of auxiliary value functions indexed by Lagrange multipliers . We also present a series of numerical examples.
R
dividend payments
dividends
R
(P1). We use the Lagrangian dual function which leads to an auxiliary problem (P2). For this problem, given a multiplier \Lambda, we prove the uniqueness of the optimal barrier strategy and we also obtain its value function. Finally, we prove that the
. We introduce the dual problem and show that the complementary slackness conditions are satisfied, thus there is no duality gap. Therefore the
R
of (P1) is
can be
R
over \Lambda of all value functions of problems (P2)
of auxiliary value functions indexed by Lagrange multipliers