In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Mar...In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes.展开更多
基金Project supported by the Russian Foundation for Basic Research,Grant 99-01-00847the Russian Humanitarian Scientific Foundation,Grant 00-02-00152a,by the NNSF of China(19971047) and DSF
文摘In this paper,the asymptotic behavior of generalized risk processes without any momentassumptions on the controlling process is described.
基金Supported by National Natural Science Foundations of China(10271062,10571092)a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.HKU 7475/05H)
文摘In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes.
