Abstract
This paper focuses on stochastic orders and its applications: policy limits and deductibles. Further, many applications and some examples are given: comparison of two families of copulas, individual and collective risk model, reinsurance contracts and dependent portfolios increase risk. More precisely, we propose a new model for insurance risks while we give some properties. To this end, we obtain the ordering of the optimal allocation of policy limits and deductibles for this model.Modern actuarial theory and practice risks plays a crucial role in the economy and nance. The principal goal of the actuaries is the determination of the distribution function of a sum of random variables. In general the random variables are assumed to be mutually independent.
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