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Minimizing upper bound of ruin probability under discrete risk model with Markov chain interest rate. (English) Zbl 1338.60184

Summary: This article focuses on a minimal upper bound of the ruin probability for a discrete-time risk model with Markov chain interest rate and stochastic investment return. The interest rate of the bond market is assumed to be a stationary Markov chain, and the return process of a stock market can be negative. This article presents two kinds of methods for minimizing the upper bound of the ruin probability. One method relies on recursive equations for finite time ruin probabilities and an inductive approach, the other one depends on a martingale approach. Numerical examples show that the martingale approach is better than the inductive one.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60K05 Renewal theory
60G42 Martingales with discrete parameter
91B30 Risk theory, insurance (MSC2010)
93E20 Optimal stochastic control
60J22 Computational methods in Markov chains
65C40 Numerical analysis or methods applied to Markov chains
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[1] DOI: 10.1287/moor.20.4.937 · Zbl 0846.90012 · doi:10.1287/moor.20.4.937
[2] DOI: 10.1016/j.insmatheco.2004.06.004 · Zbl 1122.91340 · doi:10.1016/j.insmatheco.2004.06.004
[3] Flemming W.H., Controlled Markov processes and viscosity solutions (1993)
[4] Gaier J., Ann. Appl. Probab. 3 pp 1054– (2003)
[5] DOI: 10.1007/978-1-4613-9058-9 · doi:10.1007/978-1-4613-9058-9
[6] DOI: 10.3934/jimo.2007.3.155 · Zbl 1137.93056 · doi:10.3934/jimo.2007.3.155
[7] DOI: 10.1016/S0167-6687(00)00049-4 · Zbl 1007.91025 · doi:10.1016/S0167-6687(00)00049-4
[8] DOI: 10.1007/s007800200095 · Zbl 1069.91051 · doi:10.1007/s007800200095
[9] DOI: 10.1016/S0167-6687(99)00052-9 · Zbl 1103.91366 · doi:10.1016/S0167-6687(99)00052-9
[10] DOI: 10.1016/S0304-4149(01)00148-X · Zbl 1058.60095 · doi:10.1016/S0304-4149(01)00148-X
[11] DOI: 10.1080/10920277.2004.10596134 · Zbl 1085.60511 · doi:10.1080/10920277.2004.10596134
[12] Lu G., J. Ind. Manage. Opt. 1 pp 280– (2005)
[13] DOI: 10.1080/03461238.1994.10413927 · Zbl 0802.62090 · doi:10.1080/03461238.1994.10413927
[14] DOI: 10.1080/03461230110106507 · Zbl 1141.91031 · doi:10.1080/03461230110106507
[15] DOI: 10.1007/s00186-005-0445-2 · Zbl 1101.93087 · doi:10.1007/s00186-005-0445-2
[16] DOI: 10.1214/aoap/1031863173 · Zbl 1021.60061 · doi:10.1214/aoap/1031863173
[17] DOI: 10.1016/j.insmatheco.2005.06.009 · Zbl 1129.91020 · doi:10.1016/j.insmatheco.2005.06.009
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