Uncertain insurance risk process with multiple premium processes and single claim process

Insurance risk process is usually used to describe the risk of an insurance company based on some criteria such as ruin index, ruin time and deficit. This paper first presents an insurance risk process with multiple premium processes, in which the multiple classes of premium processes and claim process are modeled by uncertain renewal reward processes. Afterwards, the analytical formula of ruin index and the uncertainty distribution of ruin time are derived separately. Besides, some examples are also given to illustrate the results.