🤖 AI Summary
This paper addresses the problem of designing time-consistent optimal investment strategies under an explicit deviation-based conditional value-at-risk (DCVaR) constraint in continuous-time portfolio optimization—specifically, controlling the difference between terminal wealth’s CVaR and its expectation. To overcome the time-inconsistency inherent in conventional mean-CVaR frameworks, the paper introduces a novel methodology: within a complete market setting, it employs martingale methods to rigorously formulate and preserve the explicit DCVaR constraint, integrating convex optimization with stochastic analysis. The resulting optimal terminal wealth distribution is analytically tractable. The main contribution lies in establishing a dynamically consistent strategy with clear economic interpretation—namely, a state-dependent two-fund separation structure—that enhances both operational feasibility and robustness of risk-constrained asset allocation.
📝 Abstract
We study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR framework has been widely explored, its time-inconsistency complicates the use of dynamic programming. We follow the martingale approach in a complete market setting, as in Gao et al. [4], and extend it by retaining an explicit DCVaR constraint in the problem formulation. The optimal terminal wealth is obtained by solving a convex constrained minimization problem. This leads to a tractable and interpretable characterization of the optimal strategy.