It is well known that if a random vector with given marginal distributions is comonotonic, it has the largest sum with respect to the convex order. In this paper, we prove that the converse is also true, provided that each marginal distribution is continuous.

In this paper, we study stochastic orders of scalar products of random vectors. Based on the study of Ma [Ma, C., 2000. Convex orders for linear combinations of random variables. J. Statist. Plann. Inference 84, 11-25], we first obtain more general conditions under which linear combinations of...

In this paper, we study the problems of optimal allocation of policy limits and deductibles. Several objective functions are considered: maximizing the expected utility of wealth assuming the losses are independent, minimizing the expected total retained loss and maximizing the expected utility...

In the literature, orderings of optimal allocations of policy limits and deductibles were established with respect to a policyholder's preference. However, from the viewpoint of an insurer, the orderings are not enough for the purpose of pricing. In this paper, by applying the equivalent utility...

In this article, we study two optimization problems. The first is finding the best L1-approximant of a given random vector on some affine subspaces subject to a measurability condition. The second is finding the optimal allocation of policy limits such that the expected retained loss is...

In this article, we study a new notion called upper comonotonicity, which is a generalization of the classical notion of comonotonicity. A random vector is upper-comonotonic if its components are moving in the same direction simultaneously when their values are greater than some thresholds. We...

In this article, we show that some important implications concerning comonotonic couples and corresponding convex order relations for their sums cannot be translated to counter-monotonicity in general. In a financial context, it amounts to saying that merging counter-monotonic positions does not...