Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation

Asmussen, Søren; Højgaard, Bjarne; Taksar, Michael

doi:10.1007/s007800050075

Cited by 225 publications

(110 citation statements)

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“…The optimality of the "bands strategy" was recently established by Albrecher and Thonhauser [9] in the presence of fixed interest rates as well. For related work considering both excess-of-loss reinsurance and dividend distribution policies (e.g., in a diffusion setting), see [10,11] and the references included in this papers; and for work including also a utility function, see [12].…”

Section: Introductionmentioning

confidence: 99%

Dividend Problem with Parisian Delay for a Spectrally Negative Lévy Risk Process

Czarna

Palmowski

2013

J Optim Theory Appl

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In this paper, we consider dividend problem for an insurance company whose risk evolves as a spectrally negative Lévy process (in the absence of dividend payments) when a Parisian delay is applied. An objective function is given by the cumulative discounted dividends received until the moment of ruin, when a so-called barrier strategy is applied. Additionally, we consider two possibilities of a delay. In the first scenario, ruin happens when the surplus process stays below zero longer than a fixed amount of time. In the second case, there is a time lag between the decision of paying dividends and its implementation.

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Section: Introductionmentioning

confidence: 99%

Dividend Problem with Parisian Delay for a Spectrally Negative Lévy Risk Process

Czarna

Palmowski

2013

J Optim Theory Appl

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“…The assumption is that the dividend follows an exponential process which is commonly used on measuring dividend growth in finance (Asmussen et al, 2000;Albrecher et al, 2005;Avanzi, 2009). Therefore, the dividend d t is a continuous random variable with the probability density function of an exponential distribution as…”

Section: Basic Setupmentioning

confidence: 99%

Incentives and Adaptive Expectations in a Financial Market with Heterogenous Agents

Wang

2015

SSRN Journal

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This paper establishes an agent-based model to describe the dynamic behaviour of the financial market with mutual fund managers and investors under two types of compensation contracts: asset-based fees and performance-based fees, and using two types of adaptive expectation: trend chaser and contrarian. Our results show that both of trading strategies of trend chaser and contrarian destabilise the market. However, trend chasers always trigger significant fluctuations, while contrarian traders bring along the slight up and down oscillations. The types of compensation contracts change the behaviour of contrarian traders, but have no influence to trend chaser. We also find that inertia parameter decrease the stability of market and induce market price to be underestimated. In particular, the heterogenous analysis under different compensation contracts shows that asset maximisers dominate the whole market and produce higher returns, which can be used to explain the current situation in real market that most of mutual funds choose asset-based contract.Moreover, the coexistence of two compensation schemes may amplify market fluctuations and create bubbles.

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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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Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation

Cited by 225 publications

References 20 publications

Dividend Problem with Parisian Delay for a Spectrally Negative Lévy Risk Process

Dividend Problem with Parisian Delay for a Spectrally Negative Lévy Risk Process

Incentives and Adaptive Expectations in a Financial Market with Heterogenous Agents

On optimal control of capital injections by reinsurance and investments

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