Comparison of combined stochastic risk processes and its applications

In this article we compare combined stochastic risk processes and consider its applications to various fields of relevance. Initially, the problem is formulated in terms of optimal transportation under fatal risks which may cause the failure of the transportation. Various transportation policies are considered and the problem of determining optimal policy maximizing the probability of success of transportation is suggested. Then the suggested problem is reformulated in the context of reliability modelling under more general settings and the main results are derived. Applications of the results to many different areas are discussed.