Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example

Jgaard, Bjarne Hø; Taksar, Michael

doi:10.1111/1467-9965.00066

Cited by 203 publications

(153 citation statements)

References 28 publications

(39 reference statements)

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“…In addition, as in Lemma 2.1 of Højgaard and Taksar [29], it shows that 1 ≥ 0 if and only if ≥ /2 + 2 / .…”

Section: The Casesupporting

confidence: 52%

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The Optimal Dividend Payout Model with Terminal Values and Its Application

Luo

Chen

2017

Mathematical Problems in Engineering

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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.

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“…In addition, as in Lemma 2.1 of Højgaard and Taksar [29], it shows that 1 ≥ 0 if and only if ≥ /2 + 2 / .…”

Section: The Casesupporting

confidence: 52%

“…By the similar arguments of Højgaard and Taksar [29], the HJB equation (14) can be derived. To avoid tedious repetition, here we omit it.…”

Section: The Hamilton-jacobi-bellman Equation and Its Solutionmentioning

confidence: 98%

The Optimal Dividend Payout Model with Terminal Values and Its Application

Luo

Chen

2017

Mathematical Problems in Engineering

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“…The special case of constant drift and diffusion coefficient was then solved again by slighty different means in Jeanblanc-Piqué & Shiryaev [73] and Asmussen & Taksar [12] (Radner & Shepp [102] study the situation where the drift and volatility can also be controlled within a discrete set of possible values). In addition to the dividend control, Højgaard & Taksar [68,69] also considered the possibility of proportional reinsurance and optimal investment. For an overview on this and variants of these problems for diffusion processes see Taksar [116].…”

Section: Value Functionsmentioning

confidence: 99%

Optimality results for dividend problems in insurance

Albrecher

Thonhauser

2009

Rev. R. Acad. Cien. Serie A. Mat.

145

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“…In many later papers the problem was formulated and solved also for a diffusion approximation, see Shreve at al. [72], Jeanblanc-Picqué and Shiryaev [46], Paulsen and Gjessing [57], Højgaard and Taksar [38], Asmussen and Taksar [3], Asmussen et al [4], Paulsen [58].…”

Section: Measuring Risksmentioning

confidence: 99%

On optimal control of capital injections by reinsurance and investments

Eisenberg¹

2010

Blätter DGVFM

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AcknowledgementsI would like to express my thanks to my supervisor Prof. Dr. Hanspeter Schmidli. I have greatly profited from his hints and suggestions generously given during our conversations. I am very grateful to Prof. Dr. Josef Steinebach who agreed to be coreferent.I would like to acknowledge Markus Schulz for his listening ear and Mrs Anderka for believing in me.In particular, I would like to thank my family who has supported me all the time and enabled a successful completion of this work. AbstractAn insurance company, having an initial capital x, cashes premiums continuously and pays claims of random sizes at random times. In addition to that, the company can buy reinsurance or/and invest money into a riskless or risky assets. The company holders are confronted with the problem of taking decisions on a business policy of the company. Thus, a measure for the risk connected with an insurance portfolio is sorely needed.The ruin probability, i.e. the probability that the surplus process becomes negative in finite time, is typically the measure for an insurance company's solvency. However, the ruin probability approach has been criticised among other things for not considering the severity of an insolvency and for ignoring the time value of money.An alternative to measure the risk of a surplus process is to consider the value of expected discounted capital injections, which are necessary to keep the process above zero. Naturally, it raises the question how to minimise this value. If the company holders prefer (or are indifferent) investing tomorrow to investing today, it is optimal to inject capital only when the surplus becomes negative and only as much as is necessary to keep the process above zero.In the first part of this work, we solve the problem of minimising the expected discounted capital injections over all dynamic reinsurance strategies for the classical risk model and its diffusion approximation. In the second part, we extend the concept by adding the possibility of investing money, if the surplus remains positive, into a riskless asset. In these two cases we are able to show the existence and uniqueness of the optimal reinsurance strategy and the value function as the minimising value of expected discounted capital injections.In the third part, we consider the surplus process, where the company holders can invest money into a risky asset modeled as a Black-Scholes model. The forth part extends the setup of the third part by possibility of reinsurance. In the last two cases we solve the problem explicitly only for the case of diffusion approximation. In the classical risk model the concept of viscosity solutions introduced by Crandall and Lions has been used.All the studies are illustrated by simulations, written in Java. Als alternatives Risikomaß betrachtet man den Wert der erwarteten diskontierten Kapitalzuführungen, welche notwendig sind damit derÜberschussprozess nichtnegativ bleibt. Es stellt sich die Frage, wie man diesen Wert minimiert. Wir nehmen an, dass die Inhaber der Versicherungsges...

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Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example

Cited by 203 publications

References 28 publications

The Optimal Dividend Payout Model with Terminal Values and Its Application

The Optimal Dividend Payout Model with Terminal Values and Its Application

Optimality results for dividend problems in insurance

On optimal control of capital injections by reinsurance and investments

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