3. RUIN RESERVS

5. Our Equation Method of successive approximations For example…

6. Let us have K-th iteration

7. This is time grid

8. To obtain we use values of in grid nodes

9. And so on…

10. To obtain we use values of in grid nodes And so on… just the same way

11. Due to independent nature of calculations we can use more then one core (up to number of greed nodes)…. To obtain we use values of in grid nodes

12. And as a result we can interpolate

13. RUIN RESERVS We need millions of such simulations! For real time modelling we need parallelization

14. Parallel actuarial simulations Random outcome= Company simulation (Inputs) Inputs – hundreds Simulations – millions Example: Ruin Probability= Fraction of ruined trajectories

16.  Realistic simulation models  Adjusted to law regulations  Real world data  Optimization over any parameter (multi criteria task)  Based on parallel simulations  GPU accelerated - powered by CUDA  User friendly

18. Just an α version…

19. Probability of insolvency (Ruin) as a function of parameter (dividend rate)

20. Resudual capital and dividends as functions of parameter (dividend rate)

21. Efficient frontier (Profit vs Risk) allows to select a tradeoff point

22. Per quarter normalized claim statistics of a well- known Ukrainian insurance company with foreign capital.

26. Insurance simulation model based on real world data. Risk/Profit optimization (Efficient frontier constructing) Any parameter can be an optimization variable. Real time GPU accelerated Monte Carlo method. (about 1 second for billions of trajectories) And at last User friendly interface turns RMS 0.2 in a very efficient and nice system

27. Kaufmann R., Gadmer A., Klett R. Introduction to dynamic financial analysis // ASTIN Bulletin, Vol. 31, No. 1, 2001, pp. 213-249. Norkin B. Parallel computations in insurance business optimization //Proceedings of the 1-st International Conference on High Performance Computing. October 12-14, 2011, Kyiv, Ukraine. – P. 33- 39. Норкин Б.В. Распараллеливание методов оценки риска банкротства страховой компании // Теорія оптимальних рішень. – Київ : Інститут Кібернетики, 2010. – Стор. 33-39. Норкин Б.В. О вероятности разорения управляемого процесса авторегрессии // Комп’ютерна математика. Ін-т кібернетики ім. В.М. Глушкова. Київ, 2011. – С. 142-150.