Research On Several Dual Models

Risk theory is an important branch of modern mathematics, is also a very important topic oftoday’s mathematics. With the continuous growth and development of insurance industry, riskmodels are updating and improving on and on, many scholars have already made a lot ofresearch results. Take the various new factors in the insurance operation into account, it isnecessary to research on some special cases of the dual risk models in depth.The paper carries out analysis on dual risk model under three different conditions. Adopthomogeneous Poisson process, martingale method, other common mathematical research toolsand methods to carry out analysis on positive and negative risk model, Poisson risk model withinterference and dual re-insurance model respectively. Research on some basic characteristics,such as adjustment coefficients, upper and lower bounds of adjustment coefficients, bankruptcyprobabilities, some cases of adjustment coefficients while claims are exponentially distributedand a series of relevant problems. Furthermore, make consistent conclusions with some classicalmodel through simulation values and specific examples.