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This paper focuses on new measures of performance in single-server Markovian queueing system. These measures depend on the moments of order statistics. The expected value and the variance of the maximum (minimum) number of customers in the system as well as the expected value and the variance of the minimum (maximum) waiting time are presented. Application to an M/M/1 model is given to illustrate the idea and the applicability of the proposed measures.

We propose asset and liability management models in which the risk of underfunding is modelled based on the concept of stochastic dominance. Investment decisions are taken such that the distribution of the funding ratio, that is, the ratio of asset to liabilities, is non-dominated with respect to second order stochastic dominance. In addition, the funding ratio distribution is close in an optimal sense to a user-specified target distribution. Interesting results are obtained when the target distribution is degenerate; in this case, we can obtain equivalent risk minimisation models, with risk defined as expected shortfall or as worst case loss. As an application, we consider the financial planning problem of a defined benefit pension fund in Saudi Arabia.