62 research outputs found
Convexity of ruin probability and optimal dividend strategies for a general Levy process
In this paper, we consider the optimal dividends problem for a company whose
cash reserves follow a general Levy process with certain positive jumps and
arbitrary negative jumps. The objective is to find a policy which maximizes the
expected discounted dividends until the time of ruin. Under appropriate
conditions, we appeal to very recent results in the theory of potential
analysis of subordinators to obtain the convexity properties of probability of
ruin. We present conditions under which the optimal dividend strategy, among
all admissible ones, takes the form of a barrier strategy.Comment: 19 pages, corrected some typo
Optimal financing and dividend distribution in a general diffusion model with regime switching
We study the optimal financing and dividend distribution problem with
restricted dividend rates in a diffusion type surplus model where the drift and
volatility coefficients are general functions of the level of surplus and the
external environment regime. The environment regime is modeled by a Markov
process. Both capital injections and dividend payments incur expenses. The
objective is to maximize the expectation of the total discounted dividends
minus the total cost of capital injections. We prove that it is optimal to
inject capitals only when the surplus tends to fall below zero and to pay out
dividends at the maximal rate when the surplus is at or above the threshold
dependent on the environment regime
On non-trivial barrier solutions of the dividend problem for a diffusion under constant and proportional transaction costs
In Bai and Paulsen (SIAM J. Control optim. 48, 2010) the optimal dividend
problem under transaction costs was analyzed for a rather general class of
diffusion processes. It was divided into several subclasses, and for the
majority of subclasses the optimal policy is a simple barrier policy; whenever
the process hits an upper barrier , reduce it to
through a dividend payment. After transaction costs, the shareholder receives
.
It was proved that a simple barrier strategy is not always optimal, and here
these more difficult cases are solved. The optimal solutions are rather
complicated, but interesting
The Optimal Dividend Payout Model with Terminal Values and Its Application
For some firms with large nonliquid assets, preferred shareholders can still get back a little bit of money when the firms finish disbursement of loans at the status of bankruptcy. For such a situation, to investigate the optimal dividend policy, a stochastic dynamic dividend model with nonzero terminal bankruptcy values is put forward in this paper. Moreover, an analytic solution for the optimal objective function of the discounted dividends is provided and verified. An important application of this result is that it can be employed to construct the solution for the optimal value function on the dividend problem with bailouts at bankruptcy. Further, the relationship for the solutions of these two different problems is demonstrated. In the end, some numerical examples are provided to support our theoretical results and the corresponding economic interpretations are illustrated
Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model
This paper considers the optimal dividend payment problem in
piecewise-deterministic compound Poisson risk models. The objective is to
maximize the expected discounted dividend payout up to the time of ruin. We
provide a comparative study in this general framework of both restricted and
unrestricted payment schemes, which were only previously treated separately in
certain special cases of risk models in the literature. In the case of
restricted payment scheme, the value function is shown to be a classical
solution of the corresponding HJB equation, which in turn leads to an optimal
restricted payment policy known as the threshold strategy. In the case of
unrestricted payment scheme, by solving the associated integro-differential
quasi-variational inequality, we obtain the value function as well as an
optimal unrestricted dividend payment scheme known as the barrier strategy.
When claim sizes are exponentially distributed, we provide easily verifiable
conditions under which the threshold and barrier strategies are optimal
restricted and unrestricted dividend payment policies, respectively. The main
results are illustrated with several examples, including a new example
concerning regressive growth rates.Comment: Key Words: Piecewise-deterministic compound Poisson model, optimal
stochastic control, HJB equation, quasi-variational inequality, threshold
strategy, barrier strateg
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