Joint and supremum distributions in the compound binomial model with Markovian environment. (English) Zbl 1249.91061
Summary: We study the compound binomial model in Markovian environment, which was proposed by H. Cossette, H. Landriault and È. Marceau [Scand. Actuar. J. 2003, No. 4, 301–323 (2003; Zbl 1092.91040)]. We obtain a recursive formula of the joint distribution of \(T\), \(X(T-1)\) and \(|X(T)|\) (i.e., the time of ruin, the surplus before ruin and the deficit at ruin) by the method of mass function of up-crossing zero points, as given by G. Liu and J. Zhao [Insur. Math. Econ. 40, No. 1, 95–103 (2007; Zbl 1107.60303)]. By using the same method, an recursive formula for the supremum distribution is obtained. An example is included to illustrate the results of the model.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
Keywords:
compound binomial model; Markovian environment; joint distribution; mass function; recursive formula; supremum distributionReferences:
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