We are interested in the tail behavior of the randomly weighted sum ∑i=1 n θi Xi, in which the primary random variables X1, …, Xn are real valued, independent and subexponentially distributed, while the random weights θ1, …, θn are nonnegative and arbitrarily dependent, but independent of X1, …, Xn. For various important cases, we prove that the tail probability of ∑i=1 n θiXi is asymptotically equivalent to the sum of the tail probabilities of θ1X1, …, θnXn, which complies with the principle of a single big jump. An application to capital allocation is proposed.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Engineering (miscellaneous)
- Economics, Econometrics and Finance (miscellaneous)