Multi-period Value-at-Risk Constrained Portfolio Optimization via DC Programming
Abstract
We study a multi-period portfolio optimization problem with finite-scenario Value-at-Risk (VaR) constraints, transaction costs, and diversification regularization. Using a finite-scenario VaR--CVaR identity, we derive a penalized difference-of-convex (DC) formulation over the underlying convex portfolio set. To solve the resulting nonsmooth and nonconvex problem, we propose a projected inertial Boosted Difference-of-Convex Functions Algorithm (iBDCA) that combines inertial extrapolation, an objective safeguard, and a boosted line search. We prove that the method is well defined, generates a monotonically decreasing objective sequence, and has only critical accumulation points for the penalized DC problem. Under a local no-ties condition at an accumulation point, we further establish whole sequence convergence with a local R-linear rate. Numerical experiments compare iBDCA with DCA and standard BDCA on matched problem instances. Out-of-sample backtests additionally include equal-weight and buy-and-hold benchmarks to illustrate the trade-offs among realized return, risk, transaction costs, and empirical VaR control.
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BibTeX
@misc{nguyen2026multiperiod,
title = {{Multi-period Value-at-Risk Constrained Portfolio Optimization via DC Programming}},
author = {Thi Thu Van Nguyen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.13748},
eprint = {2608.13748},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.13748},
}
RIS
TY - UNPB
TI - Multi-period Value-at-Risk Constrained Portfolio Optimization via DC Programming
AU - Thi Thu Van Nguyen
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2608.13748
UR - https://arxiv.org/abs/2608.13748
AB - We study a multi-period portfolio optimization problem with finite-scenario Value-at-Risk (VaR) constraints, transaction costs, and diversification regularization. Using a finite-scenario VaR--CVaR identity, we derive a penalized difference-of-convex (DC) formulation over the underlying convex portfolio set. To solve the resulting nonsmooth and nonconvex problem, we propose a projected inertial Boosted Difference-of-Convex Functions Algorithm (iBDCA) that combines inertial extrapolation, an objective safeguard, and a boosted line search. We prove that the method is well defined, generates a monotonically decreasing objective sequence, and has only critical accumulation points for the penalized DC problem. Under a local no-ties condition at an accumulation point, we further establish whole sequence convergence with a local R-linear rate. Numerical experiments compare iBDCA with DCA and standard BDCA on matched problem instances. Out-of-sample backtests additionally include equal-weight and buy-and-hold benchmarks to illustrate the trade-offs among realized return, risk, transaction costs, and empirical VaR control.
ER -