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stop-loss reinsurance with distribution-free approximation
Published in Yuli Rahmawati, Peter Charles Taylor, Empowering Science and Mathematics for Global Competitiveness, 2019
S. Nurrohmah Adhariyansyah, S.M. Soemartodjo
Stop-loss reinsurance is a reinsurance in which the insurance company will determine its retention limit, and the reinsurance company will cover the risks that exceed the retention limit. Technically, if the losses that are received by the insurance company are below the retention limit, then the insurance company will cover the risks itself. Otherwise, if the losses that are received by the insurance company are above the retention limit, then the insurance company will transfer the risks that cannot be covered to the reinsurance company. After that, the reinsurance company will charge a reinsurance premium to the insurance company as a guarantee of risk that has been transferred to the reinsurance company. This reinsurance premium will depend on the retention limit that is determined by the insurance company.
Changing Flood Risk – A Re-insurer’s Viewpoint
Published in Zbigniew W. Kundzewicz, Changes in Flood Risk in Europe, 2019
Just like private individuals, insurance companies try to avoid volatility in their payments. Natural perils insurance is highly volatile. Large single losses (produced by one event) can be mitigated if part of the risk is transferred to the reinsurance sector, in which many companies transact business on a worldwide scale. If catastrophic losses occur in one country, the impact is distributed throughout the world, thus relieving the burden on the local insurance market and possibly even preventing its collapse. Reinsurance is quite simply insurance for insurance companies. A company has to be aware of its possible maximum losses in order to maintain a healthy balance sheet and even to ensure its survival. Since the theoretically possible maximum losses are not actually encountered, the “probable maximum losses” (PML) are assessed. What is “probable” is determined by a company’s business policy, and ranges – as a rule – from 1-in-200 to 1-in-1000 years. Losses are modelled stochastically by computing losses from a large number of artificially-generated single events, where the statistics relating to the frequency, intensity, and geographical extent are based on past observations (Willems, 2005; Kron & Ellenrieder, 2009).
Invited lecture: Risk zonation and loss accumulation analysis for floods
Published in Zhao-Yin Wang, Shi-Xiong Hu, Stochastic Hydraulics 2000, 2020
Billion-dollar catastrophes cannot be born by a local insurance market without major damage to the insurance industry itself. Even in strong markets such as the United States, great events leave their traces. Hurricane Andrew wiped out 13 primary insurance companies in the American Southeast in 1992. The burden from claims exceeded by far the capacity of these companies, and they went bankrupt. To prevent such things from happening and to protect themselves from bankruptcy, insurance companies must assess the maximum probable losses they may be confronted with and prepare for them. One – often the main – aspect of preparation is to seek reinsurance. Reinsurance is nothing but insurance for insurance companies.
Mean-variance problem for an insurer with dependent risks and stochastic interest rate in a jump-diffusion market
Published in Optimization, 2022
Concerning future related work, there are many interesting problems to discuss. One, related to this paper, is to solve the mean-variance problem in a game framework, which was proposed by Björk and Murgoci [32]. On the other hand, there are lots of different forms of reinsurance, for example, excess-of-loss reinsurance and per-claim reinsurance. Discussing the optimal form of reinsurance will make the problem more interesting and meaningful. Last but not least, one of the important premises in this paper is that the processes of bond and stock are driven by the same Brownian motion, which is related to the ability to derive the closed-form solutions of the HJB equation. Hence, it prompts us to apply some new methods, such as backward stochastic differential equation approach in the future research.
Stochastic optimal control on dividend policies with bankruptcy
Published in Optimization, 2019
Consider a probability space endowed with a filtration , which represents the information available up to time t, and any decision is made based upon this filtration. The state variable is the process of reserve asset, which denotes the liquid assets of a company. In the real world, many firms consider to do reinsurance to reduce the risk of their assets. As in Cadenillas et al. [8], we employ as the proportion of reinsurance for the liquid asset. Meanwhile, the cumulative dividend amount paid out to shareholders up to time t is denoted by . A control policy π is defined by a two-dimensional stochastic process . Under the policy π, the dynamics of the controlled reserve process is governed by with , where , , and is a standard Brownian motion. In addition, is assumed to be -measurable.
Asymptotic solution of optimal reinsurance and investment problem with correlation risk for an insurer under the CEV model
Published in International Journal of Control, 2023
Ximin Rong, Yiqi Yan, Hui Zhao
Reinsurance and investment are two important ways that insurers control risks and increase profit. Specifically, insurers usually purchase reinsurance to cede part of their claim losses to reinsurer and invest in financial market to gain profits. Therefore, the optimal reinsurance and investment problem for insurers have attracted more and more attention recently. For example, Hipp and Taksar (2000) investigate the optimal investment problem of minimising the probability of ruin under the compound Poisson risk model. Schmidli (2001) studies the optimal proportional reinsurance problem for minimising the probability of ruin. Schmidli (2002) further considers the optimisation problem that the insurer can invest in a financial market and purchase proportional reinsurance. Yang and Zhang (2005) study the optimal investment policy for an insurer with a jump-diffusion risk process. Bai and Guo (2008) consider an optimal proportional reinsurance and investment problem with multiple risky assets under the constraint of no-shorting. Chen et al. (2010) study an optimal reinsurance-investment problem for an insurance company with a dynamic Value-at-Risk (VaR) constraint. Zeng and Li (2011) investigate an optimal time-consistent reinsurance and investment problem under a mean–variance criterion. Peng et al. (2014) consider the optimal investment, consumption and proportional reinsurance problem for an insurer with option type payoff at the terminal time under the criterion of exponential utility maximisation. Huang et al. (2016) study the optimal proportional reinsurance and investment problem for a jump-diffusion risk model with the no-shorting constraint and the net profit condition. Z. B. Zhou et al. (2019) investigate the multi-period reinsurance and investment optimisation problem with a serially correlated returns structure under the traditional mean–variance criterion.