Abstract
In this paper, we study a new class of dynamic risk measures for processes. These new risk measures are derived for the portfolio vectors and adapted to a given filtration. By introducing the notion of discount factor, we deeply analyze the property of cash sub-additivity for these risk measures. Furthermore, by expanding the risk position space, we derive the relationship between these new risk measures and the dynamic convex risk measures introduced by Wei & Hu [(2014) Coherent and convex risk measures for portfolios with applications, Statistics & Probability Letters 90, 114–120]. At last, we establish the representation results for them by making full use of the relationship.
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