Dynamic Portfolio Selection with Range Value-at-Risk under Logarithmic Returns

This paper focuses on the dynamic portfolio selection problem using Range Value-at-Risk (RVaR) in a continuous-time financial market, where performance and risk are measured by logarithmic returns. It transforms dynamic optimization into a static quantile problem, and characterizes the convex hull of optimal terminal wealth through quantile representation, Lagrangian optimization, and convexification methods. The study finds that pure RVaR minimization may allocate zero terminal wealth under extremely adverse states, clarifies how interval quantile risk control shapes state-dependent portfolio returns, and bridges the limiting cases of RVaR with VaR and ES.