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Optimal reinsurance policies for an insurer with a bivariate reserve risk process in a dynamic setting

Bai, Lihua ; Cai, Jun ; Zhou, Ming

Insurance, mathematics & economics, 2013-11, Vol.53 (3), p.664-670 [Periódico revisado por pares]

Amsterdam: Elsevier B.V

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  • Título:
    Optimal reinsurance policies for an insurer with a bivariate reserve risk process in a dynamic setting
  • Autor: Bai, Lihua ; Cai, Jun ; Zhou, Ming
  • Assuntos: Approximation ; Common shock model ; Dynamics ; Excess-of-loss reinsurance ; HJB equation ; Insurance policies ; Martingale central limit theorem ; Mathematical models ; Multidimensional analysis ; Probability ; Reinsurance ; Retention ; Risk management ; Ruin probability ; Studies ; Theorems ; Two-dimensional Brownian motion ; Two-dimensional compound Poisson process ; Two-dimensional diffusion approximation
  • É parte de: Insurance, mathematics & economics, 2013-11, Vol.53 (3), p.664-670
  • Notas: ObjectType-Article-2
    SourceType-Scholarly Journals-1
    ObjectType-Feature-1
    content type line 23
  • Descrição: Assume that an insurer has two dependent lines of business. The reserves of the two lines of business are modeled by a two-dimensional compound Poisson risk process or a common shock model. To protect from large losses and to reduce the ruin probability of the insurer, the insurer applies a reinsurance policy to each line of business, thus the two policies form a two-dimensional reinsurance policy. In this paper, we investigate the two-dimensional reinsurance policy in a dynamic setting. By using the martingale central limit theorem, we first derive a two-dimensional diffusion approximation to the two-dimensional compound Poisson reserve risk process. We then formulate the total reserve of the insurer by a controlled diffusion process and reduce the problem of optimal reinsurance strategies to a dynamic control problem for the controlled diffusion process. Under this setting, we show that a two-dimensional excess-of-loss reinsurance policy is an optimal form that minimizes the ruin probability of the controlled diffusion process. By solving a HJB equation with two dependent controls, we derive the explicit expressions of the optimal two-dimensional retention levels of the optimal two-dimensional excess-of-loss reinsurance policy and the minimized ruin probability. The results show that optimal dynamic two-dimensional retention levels are constant and the optimal retention levels are related by a deterministic function. We also illustrate the results by numerical examples. •We investigate the two-dimensional reinsurance policy in a dynamic setting.•By using martingale central limit theorem, a 2-dimensional diffusion is derived.•2-dimensional excess-of-loss reinsurance is optimal to minimize ruin probability.•The optimal policy and the minimized ruin probability are obtained in closed form.•The results are illustrated by numerical examples.
  • Editor: Amsterdam: Elsevier B.V
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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