An Extension of One-Period Nash Equilibrium Model in Non-Life Insurance Markets

G.  Battulga; G.  Battur; L.  Altangerel

doi:10.4236/am.2018.912087

G. Battulga¹, L. Altangerel²^*, G. Battur¹

Abstract:

This paper deals with an extension of the one-period model in non-life insurance markets (cf. [1]) by using a transition probability matrix depending on some economic factors. We introduce a multi-period model and in each period the solvency constraints will be updated. Moreover, the model has the inactive state including some uninsured population. Similar results on the existence of premium equilibrium and sensitivity analysis for this model are presented and illustrated by numerical results.

Keywords: Nash Equilibrium Model, Variational Inequalities, Transition Matrix, Non-Life Insurance Markets

Cite this paper: Battulga, G. , Altangerel, L. and Battur, G. (2018) An Extension of One-Period Nash Equilibrium Model in Non-Life Insurance Markets. Applied Mathematics, 9, 1339-1350. doi: 10.4236/am.2018.912087.

References

[1] Dutang, C., Albrecher, H. and Loisel, S. (2013) Competition among Non-Life Insurers under Solvency Constraints: A Game-Theoretic Approach. The European Journal of Operational Research, 231, 702-711.
https://doi.org/10.1016/j.ejor.2013.06.029

[2] Albrecher, H. and Dalit, D-A. (2017) On Effects of Asymmetric Information on Non-Life Insurance Prices under Competition. International Journal of Data Analysis Techniques and Strategies, 9, 287-299.
https://doi.org/10.1504/IJDATS.2017.088355

[3] Boonen, T.J., Pantelous, A.A. and Wu, R. (2018) Non-Cooperative Dynamic Games for General Insurance Markets. Insurance: Mathematics and Economics, 78, 123-135.
https://doi.org/10.1016/j.insmatheco.2017.12.001

[4] Wu, R. and Pantelous, A.A. (2017) Potential Games with Aggregation in Non-Co-operative General Insurance Markets. ASTIN Bulletin, 47, 269-302.
https://doi.org/10.1017/asb.2016.31

[5] Rees, R., Gravelle, H. and Wambach, A. (1999) Regulation of Insurance Markets. The Geneva Paper on Risk and Insurance Theory, 24, 55-68.
https://doi.org/10.1023/A:1008733315931

[6] Durrett, R. (2012) Essentials of Stochastic Processes. Springer Texts in Statistics, Springer.
https://doi.org/10.1007/978-1-4614-3615-7

[7] McFadden, D. (1981) Econometric Models of Probabilistic Choice, Structural Analysis of Discrete Data with Econometric Applications. The MIT Press, 198-272.

[8] Rosen, J.B. (1965) Existence and Uniqueness of Equilibrium Points for Concave N-Person Games. Econometrica, 33, 520-534.

[9] Facchinei, F. and Pang, J.S. (2003) Finite-Dimensional Variational Inequalities and Complementarity Problems. Computational Science & Engineering, 2.

[10] Solodov, M.V. and Svaiter, B.F. (1999) A New Projection Method for Variational Inequality Problems. SIAM Journal on Control and Optimization, 37, 765-776.
https://doi.org/10.1137/S0363012997317475

[11] Altangerel, L. and Battur, G. (2012) Perturbation Approach to Generalized Nash Equilibrium Problems. Optimization Letters, 6, 1379-1391.
https://doi.org/10.1007/s11590-012-0510-8

[12] Facchinei, F. and Kanzow, C. (2010) Generalized Nash Equilibrium Problems. Annals of Operations Research, 175, 177-211.
https://doi.org/10.1007/s10479-009-0653-x