On the Riesz decomposition property and the interpolation property of stopping times

It is known that random variables have the Riesz decomposition property and the interpolation property. These properties are not only interesting in their own rights; they have been applied to quantitative finance and actuarial mathematics. One would naturally ask whether the same holds for stopping times. We give an affirmative answer in this paper. We also point out that optional times possess these two properties too.