Threshold Risk Measures Part 1: Finite Horizon

In this paper we introduce the threshold risk measures, a class of risk measures incompatible with the coherent risk measures. In particular, the threshold risk measures consider the risk involved in applications where being above a threshold (for minimization problems) is considered too risky and should be avoided as much as possible. In this paper we develop the threshold risk measures together with their dynamic counterparts and apply these to the finite horizon dynamic programming with risk measures model. We develop several Bellman-type recursive algorithms to solve the finite horizon problem dynamic problem. A second part to this paper focuses on infinite horizon problems [10].