# A dual risk model with additive and proportional gains: ruin probability and dividends.

@article{Boxma2020ADR, title={A dual risk model with additive and proportional gains: ruin probability and dividends.}, author={Onno J. Boxma and Esther Frostig and Zbigniew Palmowski}, journal={arXiv: Probability}, year={2020} }

We consider a dual risk model with constant expense rate and i.i.d. exponentially distributed gains $C_i$ ($i=1,2,\dots$) that arrive according to a renewal process with general interarrival times. We add to this classical dual risk model the proportional gain feature, that is, if the surplus process just before the $i$th arrival is at level $u$, then for $a>0$ the capital jumps up to the level $(1+a)u+C_i$. The ruin probability and the distribution of the time to ruin are determined. We…

## References

SHOWING 1-10 OF 25 REFERENCES

### On the dual risk model with Parisian implementation delays in dividend payments

- MathematicsEur. J. Oper. Res.
- 2017

### The dual risk model with dividends taken at arrival

- MathematicsInsurance: Mathematics and Economics
- 2018

### Parisian ruin for the dual risk process in discrete-time

- MathematicsEuropean actuarial journal
- 2018

A recursive expression is derived for the finite-time Parisian ruin probability, in terms of classic discrete-time dual ruin probabilities, by exploiting the strong Markov property of the risk process.

### Optimal dividends in the dual risk model under a stochastic interest rate

- Mathematics
- 2017

Optimal dividend strategy in dual risk model is well studied in the literatures. But to the best of our knowledge, all the previous works assumes deterministic interest rate. In this paper, we study…

### Optimal dividends problem with a terminal value for spectrally positive Levy processes

- Mathematics
- 2013

### ON OPTIMAL DIVIDENDS IN THE DUAL MODEL

- MathematicsASTIN Bulletin
- 2013

Abstract We revisit the dividend payment problem in the dual model of Avanzi et al. ([2–4]). Using the fluctuation theory of spectrally positive Lévy processes, we give a short exposition in which we…

### On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums

- MathematicsJ. Optim. Theory Appl.
- 2018

The mean of the cumulative discounted dividends paid until the time of ruin, if the barrier strategy is applied, is calculated in the dual risk model, dual to the risk model for insurance applications, where premiums are surplus-dependent.