Problem
Research questions and friction points this paper is trying to address.
Dynamic Portfolio Optimization
CVaR Constraints
Continuous-time
Dynamic Portfolio Optimization under CVaR Constraints
๐ค AI Summary
็ ็ฉถๅจ็ป็ซฏๆๅคฑ็CVaR็บฆๆไธ๏ผ้่ฟๅๅฑๆ็ดข็ฎๆณไผๅ่ฟ็ปญๆถ้ดๅจๆๆ่ต็ปๅ้ฎ้ข๏ผๆๅบไธ็ง้ๅๅ้ฃ้ฉ่ฐๆด็ญ็ฅใ
๐ Abstract
We study continuous-time dynamic portfolio optimization under a Conditional Value-at-Risk (CVaR) constraint on the investor's terminal loss. For a general class of convex trading objectives, we exploit the auxiliary-threshold representation of CVaR to establish the existence of an optimal strategy and strong duality without requiring market completeness. These results motivate a dual-based nested bisection--golden-search algorithm over the threshold and Lagrangian multiplier, where the inner iterations reduce to standard unconstrained stochastic control problems. We prove that the resulting strategies converge to the optimal control as the number of iterations tends to infinity. Numerical experiments recover the Merton policy when the risk constraint is nonbinding. When the constraint is binding, the optimal strategy becomes state dependent: the investor reduces risky exposure following adverse outcomes but preserves, and near maturity may increase, exposure following favorable outcomes. Thus, a terminal CVaR constraint produces an asymmetric reallocation across states rather than uniform de-risking. Nontraded endowment risk amplifies the conservative adjustment, whereas price impact lowers desired positions and adjustment speeds.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Conditional Value-at-Risk (CVaR)
dual-based nested bisection--golden-search algorithm
state-dependent strategy
asymmetric reallocation
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