scholarly journals The Optimal Time to Merge Two First-Line Insurers with Proportional Reinsurance Policies

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yanan Li ◽  
Chuanzheng Li
Keyword(s):  
Diffusion Approximation ◽  
Survival Probability ◽  
Optimal Time ◽  
Proportional Reinsurance ◽  
Approximation Model ◽  
First Line ◽  
Optimal Reinsurance ◽  
Verification Theorem

We examine the optimal time to merge two first-line insurers with proportional reinsurance policies. The problem is considered in a diffusion approximation model. The objective is to maximize the survival probability of the two insurers. First, the verification theorem is verified. Then, we divide the problem into two cases. In case 1, never merging is optimal and the two insurers follow the optimal reinsurance policies that maximize their survival probability. In case 2, the two insurers follow the same reinsurance policies as those in case 1 until the sum of their surplus processes reaches a boundary. Then, they merge and apply the merged company’s optimal reinsurance strategy.

scholarly journals The Reduction of Initial Reserves Using the Optimal Reinsurance Chains in Non-Life Insurance

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1350
Author(s):  
Galina Horáková ◽  
František Slaninka ◽  
Zsolt Simonka
Keyword(s):  
Life Insurance ◽  
Continuous Time ◽  
Ruin Probability ◽  
Proportional Reinsurance ◽  
Insurance Risk ◽  
Optimal Reinsurance ◽  
Insurance Contracts ◽  
Time Period ◽  
Different Types ◽  
Capital Injections

The aim of the paper is to propose, and give an example of, a strategy for managing insurance risk in continuous time to protect a portfolio of non-life insurance contracts against unwelcome surplus fluctuations. The strategy combines the characteristics of the ruin probability and the values VaR and CVaR. It also proposes an approach for reducing the required initial reserves by means of capital injections when the surplus is tending towards negative values, which, if used, would protect a portfolio of insurance contracts against unwelcome fluctuations of that surplus. The proposed approach enables the insurer to analyse the surplus by developing a number of scenarios for the progress of the surplus for a given reinsurance protection over a particular time period. It allows one to observe the differences in the reduction of risk obtained with different types of reinsurance chains. In addition, one can compare the differences with the results obtained, using optimally chosen parameters for each type of proportional reinsurance making up the reinsurance chain.

A diffusion approximation model of light transport in multilayered skin tissue

2007 ◽  
Author(s):  
M. Makropoulou ◽  
E. Kaselouris ◽  
E. Drakaki ◽  
A.A. Serafetinides ◽  
J. A. Sianoudis
Keyword(s):  
Diffusion Approximation ◽  
Light Transport ◽  
Skin Tissue ◽  
Approximation Model

A diffusion approximation model of light transport in multilayered skin tissue

2007 ◽  
Author(s):  
M. Makropoulou ◽  
E. Kaselouris ◽  
E. Drakaki ◽  
A. A. Serafetinides ◽  
J. A. Sianoudis
Keyword(s):  
Diffusion Approximation ◽  
Light Transport ◽  
Skin Tissue ◽  
Approximation Model
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