On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends
Abstract
:1. Introduction
2. The Model
- is the surplus level after the claims and dividends payable at time t (at the end of period ) but before the premiums receivable at time t (at the beginning of period ).
- When both dividends and claims are payable at time t, dividends are paid before claims.
- It is worth noting that dividend payments at time i are triggered by two conditions, and . No dividend is payable if at least one condition is voided.
- If , that is, by-claims always occur simultaneously with their main claims, then it reduces to the model in Tan and Yang (2006).
- If , then it reduces to the compound binomial model with time-correlation only; see, for example, Yuen and Guo (2001).
- If both and , then the model becomes an original compound binomial model.
3. Main Results
3.1. The Case of .
- X: one main claim only with p.f. f;
- : one main claim plus its by-claim with p.f. ;
- Y: one by-claim only with p.f. g;
- : one main claim, its by-claim and a delayed by-claim with p.f. ;
- : one main claim and an undetermined by-claim with p.f. ;
- : one delayed by-claim with undetermined main and by-claims with p.f. .
- Firstly, we have and .
- Additionally,
- Therefore, is a strictly increasing function on the interval that suffices to prove the existence of a unique solution to the equation .
3.2. The Case of .
- When , both surplus processes must not pay dividends in the first period.
- When , the first period may be subject to a dividend payment.
4. Final Remarks and Future Work
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Probability | Current Period | Additional Impact on the Next Period | |
---|---|---|---|
Case 1 | No claim | Nil | |
Case 2 | Main claim and by-claim | Nil | |
Case 3 | Main claim | By-claim |
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Wat, K.P.; Yuen, K.C.; Li, W.K.; Wu, X. On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends. Risks 2018, 6, 6. https://doi.org/10.3390/risks6010006
Wat KP, Yuen KC, Li WK, Wu X. On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends. Risks. 2018; 6(1):6. https://doi.org/10.3390/risks6010006
Chicago/Turabian StyleWat, Kam Pui, Kam Chuen Yuen, Wai Keung Li, and Xueyuan Wu. 2018. "On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends" Risks 6, no. 1: 6. https://doi.org/10.3390/risks6010006