Joint Distribution Of The Supremum, The Infimum And The Number Of Zero In The Markov-modulated Risk Model

In fact,in many circumstances the first ruin of an insurance company is not definitive and this company can be rescued when the ruin is not too severe.In this case,professor Wu Rong and her students have discussed some distributions about the supremum,the infimum of the surplus in the Classical Risk Model.In the Markov-modulated Risk Model,the corresponding results was derived in this paper. Firstly,a Markov-modulated risk process was made into a strong Markov process with the theory of piecewise-deterministic Markov process and by introducing a supplementary variable. And then we used its strong Markovian property to derive the results what we needed.In Chapter l,we briefly reviewed the Risk Theory and its development.And the significance about this paper was expressed.In Chapter 2,we introduced the Classical Risk Model,the General Risk Model and the Markov-modulated Risk Model.In which,making the Markov-modulated risk process into a strong Markovian process is the preparation of deriving the main results.In Chapter 3,we respectively summarized the results about some distributions of the supremum,the infimum in the Classical Risk Model and the General Risk Model.From these discussions,we can notice that the same are the corresponding results,but the different are the methods. Chapter 4 is the main body of the paper,we derived the explicit expression of the joint distribution of the supremum, the infimum and the number of zero in the Markov- modulated risk model and some connected results.