Based on Invariance Principle for Brownian Motion, we obtained a closed-form expression of the ruin probability for the Discrete-Time Risk Model with Random Premiums that was recently introduced by Korzeniowski [1]. We show that in this model, given two strategies that have the same probability of ultimate ruin, the strategy with larger initial capital and smaller loading factor is less risky than the strategy with smaller initial capital and larger loading factor in that it lowers the probability of ruin on the finite time horizon.
References
[1]
Korzeniowski, A. (2022) Discrete Time Risk Models Financed by Random Premiums. Journal of Mathematical Finance, 12, 126-137. https://doi.org/10.4236/jmf.2022.121008
[2]
Wang, Y.Y., Yu, W.G. and Huang, Y.J. (2019) Estimating the Gerber-Shiu Function in a Compound Poisson Risk Model with Stochastic Premium Income. Discrete Dynamics in Nature and Society, 2019, Article ID: 5071268. https://doi.org/10.1155/2019/5071268
[3]
Muromskaya, A.A. (2020) Ruin in Models with Stochastic Premiums. Moscow University Matheamtics Bulletin, 75, 177-180. https://doi.org/10.3103/S0027132220040038
[4]
Nie, C.W., Chen, M. and Liu, H.Y. (2020) On a Discrete Markov-Modulated Risk Model with Random Premium Income and Delayed Claims. Mathematical Problems in Engineering, 2020, Article ID: 3042543. https://doi.org/10.1155/2020/3042543
[5]
Donsker, M.D. (1951) An Invariance Principle for Certain Probability Limit Theorems. Memoirs of American Mathematical Society, No. 6, 12.
[6]
Billingsley, P. (1999) Convergence of Probability Measures. 2nd Edition, John Wiley & Sons, Inc., New York. https://doi.org/10.1002/9780470316962
[7]
Karatzas, I. and Shreve, S.E. (1991) Brownian Motion and Stochastic Calculus, Vol. 113, 2nd Edition, Springer-Verlag, New York.
[8]
Iglehart, D.L. (1969) Diffusion Approximations in Collective Risk Theory. Journal of Applied Probability, 6, 285-292. https://doi.org/10.1017/S0021900200032800
