Complete discounted cash flow valuation

Gajek, Lesław; Kuciński, Łukasz

doi:10.1016/j.insmatheco.2016.12.004

Cited by 12 publications

(16 citation statements)

References 22 publications

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“…Concerning optimality, the proof in [20] seems unclear to us, and we wrote two messages with no answer on this point to the authors. We believe that optimality is the hardest issue in our problem, and we have provided a full (and by no means easy) proof of that.…”

Section: Remarkmentioning

confidence: 99%

“…Related literature. Among other papers dealing with similar topics like [17][18][19], the most related to ours is [20], which was brought to our attention only after completion of our paper. Ref.…”

Section: Remarkmentioning

confidence: 99%

“…Ref. [20] deals with the spectrally negative Lévy model, and the expressions for the cost functions provided in [20] are more general than ours. However, we prefer to offer here direct proofs adapted to the exponential case, for the sake of completeness.…”

Section: Remarkmentioning

confidence: 99%

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Equity Cost Induced Dichotomy for Optimal Dividends with Capital Injections in the Cramér-Lundberg Model

Avram

Goreac

et al. 2021

Mathematics

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We investigate a control problem leading to the optimal payment of dividends in a Cramér-Lundberg-type insurance model in which capital injections incur proportional cost, and may be used or not, the latter resulting in bankruptcy. For general claims, we provide verification results, using the absolute continuity of super-solutions of a convenient Hamilton-Jacobi variational inequality. As a by-product, for exponential claims, we prove the optimality of bounded buffer capital injections (−a,0,b) policies. These policies consist in stopping at the first time when the size of the overshoot below 0 exceeds a certain limit a, and only pay dividends when the reserve reaches an upper barrier b. An exhaustive and explicit characterization of optimal couples buffer/barrier is given via comprehensive structure equations. The optimal buffer is shown never to be of de Finetti (a=0) or Shreve-Lehoczy-Gaver (a=∞) type. The study results in a dichotomy between cheap and expensive equity, based on the cost-of-borrowing parameter, thus providing a non-trivial generalization of the Lokka-Zervos phase-transition Løkka-Zervos (2008). In the first case, companies start paying dividends at the barrier b*=0, while in the second they must wait for reserves to build up to some (fully determined) b*>0 before paying dividends.

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Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

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Equity Cost Induced Dichotomy for Optimal Dividends with Capital Injections in the Cramér-Lundberg Model

Avram

Goreac

et al. 2021

Mathematics

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“…Articles [GK17,AGLW20] are the only papers which relate declaring bankruptcy to the size of jumps, with general and exponential jumps, respectively. [GK17] deals also with the presence of Brownian motion and infinite activity jumps, by conditioning at the first draw-down time; the optimality proof is quite involved.…”

Section: Introductionmentioning

confidence: 99%

Optimizing dividends and capital injections limited by bankruptcy, and practical approximations for the Cramér-Lundberg process

Avram¹,

Goreac²,

Rim³

et al. 2021

Preprint

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The recent papers Gajek-Kucinsky(2017) and Avram-Goreac-Li-Wu(2020) investigated the control problem of optimizing dividends when limiting capital injections stopped upon bankruptcy. The first paper works under the spectrally negative Lévy model; the second works under the Cramér-Lundberg model with exponential jumps, where the results are considerably more explicit. The current paper has three purposes. First, it illustrates the fact that quite reasonable approximations of the general problem may be obtained using the particular exponential case studied in Avram-Goreac-Li-Wu(2020). Secondly, it extends the results to the case when a final penalty P is taken into consideration as well besides a proportional cost k > 1 for capital injections. This requires amending the "scale and Gerber-Shiu functions" already introduced in Gajek-Kucinsky(2017). Thirdly, in the exponential case, the results will be made even more explicit by employing the Lambert-W function. This tool has particular importance in computational aspects and can be employed in theoretical aspects such as asymptotics.

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“…The results of Løkka and Zervos (2008) are in Zhu and Yang (2016) extended to a general Itô diffusion model with a growth restriction for the drift function. In Gajek and Kuciński (2017) the optimal dividend problem with proportional costs for capital injection is studied under the assumption that the owner can at any time choose to liquidate the insurance company and thereby receive a liquidation value. The uncontrolled surplus process, which is defined as the surplus in excess of a parameter interpreted as a solvency capital requirement, follows a spectrally negative Lévy process.…”

Section: Introductionmentioning

confidence: 99%

Optimal dividends and capital injection under dividend restrictions

Lindensjö

Lindskog

2020

Math Meth Oper Res

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We study a singular stochastic control problem faced by the owner of an insurance company that dynamically pays dividends and raises capital in the presence of the restriction that the surplus process must be above a given dividend payout barrier in order for dividend payments to be allowed. Bankruptcy occurs if the surplus process becomes negative and there are proportional costs for capital injection. We show that one of the following strategies is optimal: (i) Pay dividends and inject capital in order to reflect the surplus process at an upper barrier and at 0, implying bankruptcy never occurs. (ii) Pay dividends in order to reflect the surplus process at an upper barrier and never inject capital-corresponding to absorption at 0-implying bankruptcy occurs the first time the surplus reaches zero. We show that if the costs of capital injection are low, then a sufficiently high dividend payout barrier will change the optimal strategy from type (i) (without bankruptcy) to type (ii) (with bankruptcy). Moreover, if the costs are high, then the optimal strategy is of type (ii) regardless of the dividend payout barrier. We also consider the possibility for the owner to choose a stopping time at which the insurance company is liquidated and the owner obtains a liquidation value. The uncontrolled surplus process is a Wiener process with drift.

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Complete discounted cash flow valuation

Cited by 12 publications

References 22 publications

Equity Cost Induced Dichotomy for Optimal Dividends with Capital Injections in the Cramér-Lundberg Model

Equity Cost Induced Dichotomy for Optimal Dividends with Capital Injections in the Cramér-Lundberg Model

Optimizing dividends and capital injections limited by bankruptcy, and practical approximations for the Cramér-Lundberg process

Optimal dividends and capital injection under dividend restrictions

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