Structural Features of Dynamic Portfolio Selection under RVaR with Logarithmic Returns
ORIGINAL / Dynamic portfolio selection under range value-at-risk with logarithmic returns
The study transforms a continuous-time mean-RVaR portfolio problem into a static quantile problem and characterizes optimal terminal wealth via a convex envelope, revealing state-dependent payoff structures induced by RVaR risk constraints. Its novelty lies in identifying two geometric configurations of the RVaR-specific convex envelope and limiting relationships to VaR and ES, offering a theoretical tool for portfolio design under interval-based quantile risk control.
01 ABSTRACT
The authors study continuous-time mean-RVaR portfolio selection with performance and risk evaluated in logarithmic returns, reducing the dynamic problem to a static quantile problem and characterizing optimal terminal wealth through an RVaR-specific convex envelope. The convex envelope exhibits two geometric configurations, corresponding to a VaR-type structure and a richer multi-region payoff structure; the RVaR solutions reduce to VaR and ES counterparts under parameter limits. Numerical results show nonlinear and generally non-monotone effects of risk parameters on risky-asset exposure, and pure minimum-RVaR optimization may assign zero terminal wealth in sufficiently bad states when α>0.
02 KEY FINDINGS
- Optimal terminal wealth is characterized by the convex envelope of an RVaR-specific transformed weighting function, which has two distinct geometric configurations corresponding to different payoff region structures.
- RVaR solutions reduce to VaR and ES solutions as β↓α and α=0, respectively, establishing theoretical links among the three risk measures.
- Closed-form wealth processes and replicating strategies are derived under constant investment opportunities; numerical results show nonlinear and generally non-monotone effects of (α,β,λ) on risky-asset exposure.
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