arXiv subjects

Nuerxiati Abudurexiti

Publications and source records attributed to Nuerxiati Abudurexiti.

6 recordsLinked to original sources

arXiv2026

Mixing-Law Uncertainty in Multivariate Normal Mean-Variance Mixtures: Semi-parametric Estimation and Robust Cumulative-Prospect Decisions

The distribution of a normal mean-variance mixture depends on the law of its positive mixing variable. We compare six parametric mixing laws with a grid nonparametric maximum likelihood estimator under the same determinant identification constraint. The mixing mean $m=\E(Z)$ is estimated and is not fixed at one. A paired block bootstrap is used to compare multivariate holdout log scores. The models that cannot be distinguished from the model with the largest score define a finite ambiguity set. We then consider a cumulative prospect problem on a common portfolio direction. For each model in the set, the NMVM representation gives a scalar projected return and a corresponding prospect-value function of the exposure. The distributionally robust decision maximizes the lower envelope of these functions. We prove existence of a solution, give the candidate points for the piecewise smooth problem, derive a reference-gap scaling result, and construct an interval branch-and-bound certificate for the finite-scenario optimum. In an application to 30 stock returns, the mixture models give higher holdout density scores than the multivariate Gaussian model. Several parametric and semi-parametric models, however, remain in the ambiguity set. The worst-case model is therefore determined at the portfolio optimization stage rather than selected in advance from a point estimate of the holdout score.

q-fin.MF↗

arXiv2026

A Finite-Candidate Distributionally Robust Tri-Objective Newsvendor Model for Energy Storage Capacity Reservation

Energy storage operators often reserve usable capacity before uncertain market opportunities are realized, for example when a day-ahead operator commits capacity for an evening peak-spread or ancillary-service window. Price spikes, renewable forecast errors, activation calls and imbalance penalties can make the decision-relevant opportunity distribution asymmetric and heavy-tailed rather than Gaussian. This paper develops a tri-objective storage-newsvendor framework for this capacity-reservation decision. The model jointly maximizes expected profit, minimizes CVaR tail loss and minimizes maximum regret over candidate non-normal distributions. We derive a critical-fractile expected-profit solution and a finite-scenario convex scalarization that solves the three objectives together. In stylized log-NMVM experiments with matched mean and variance, a moment-matched normal policy over-reserves capacity by up to 1.337 units. In a lognormal policy comparison, the CVaR and maximum-regret policies reduce tail loss and candidate-set regret at the cost of lower expected profit.

math.OC↗

arXiv2026

Two-fund separation under hyperbolically distributed returns and concave utility functions

Portfolio selection problems that optimize expected utility are usually difficult to solve. If the number of assets in the portfolio is large, such expected utility maximization problems become even harder to solve numerically. Therefore, analytical expressions for optimal portfolios are always preferred. In our work, we study portfolio optimization problems under the expected utility criterion for a wide range of utility functions, assuming return vectors follow hyperbolic distributions. Our main result demonstrates that under this setup, the two-fund monetary separation holds. Specifically, an individual with any utility function from this broad class will always choose to hold the same portfolio of risky assets, only adjusting the mix between this portfolio and a riskless asset based on their initial wealth and the specific utility function used for decision making. We provide explicit expressions for this mutual fund of risky assets. As a result, in our economic model, an individual's optimal portfolio is expressed in closed form as a linear combination of the riskless asset and the mutual fund of risky assets. Additionally, we discuss expected utility maximization problems under exponential utility functions over any domain of the portfolio set. In this part of our work, we show that the optimal portfolio in any given convex domain of the portfolio set either lies on the boundary of the domain or is the unique globally optimal portfolio within the entire domain.

q-fin.PM↗

arXiv2025

SAMP-HDRL: Segmented Allocation with Momentum-Adjusted Utility for Multi-agent Portfolio Management via Hierarchical Deep Reinforcement Learning

Portfolio optimization in non-stationary markets is challenging due to regime shifts, dynamic correlations, and the limited interpretability of deep reinforcement learning (DRL) policies. We propose a Segmented Allocation with Momentum-Adjusted Utility for Multi-agent Portfolio Management via Hierarchical Deep Reinforcement Learning (SAMP-HDRL). The framework first applies dynamic asset grouping to partition the market into high-quality and ordinary subsets. An upper-level agent extracts global market signals, while lower-level agents perform intra-group allocation under mask constraints. A utility-based capital allocation mechanism integrates risky and risk-free assets, ensuring coherent coordination between global and local decisions. backtests across three market regimes (2019--2021) demonstrate that SAMP-HDRL consistently outperforms nine traditional baselines and nine DRL benchmarks under volatile and oscillating conditions. Compared with the strongest baseline, our method achieves at least 5\% higher Return, 5\% higher Sharpe ratio, 5\% higher Sortino ratio, and 2\% higher Omega ratio, with substantially larger gains observed in turbulent markets. Ablation studies confirm that upper--lower coordination, dynamic clustering, and capital allocation are indispensable to robustness. SHAP-based interpretability further reveals a complementary ``diversified + concentrated'' mechanism across agents, providing transparent insights into decision-making. Overall, SAMP-HDRL embeds structural market constraints directly into the DRL pipeline, offering improved adaptability, robustness, and interpretability in complex financial environments.

cs.AI↗

arXiv2024

A note on closed-form spread option valuation under log-normal models

In the papers Carmona and Durrleman [7] and Bjerksund and Stensland [1], closed form approximations for spread call option prices were studied under the log normal models. In this paper, we give an alternative closed form formula for the price of spread call options under the log-normal models also. Our formula can be seen as a generalization of the closed-form formula presented in Bjerksund and Stensland [1] as their formula can be obtained by selecting special parameter values to our formula. Numerical tests show that our formula performs better for certain range of model parameters than the closed-form formula presented in Bjerksund and Stensland [1].

q-fin.MF↗

arXiv2023

Portfolio analysis with mean-CVaR and mean-CVaR-skewness criteria based on mean-variance mixture models

The paper Zhao et al. (2015) shows that mean-CVaR-skewness portfolio optimization problems based on asymetric Laplace (AL) distributions can be transformed into quadratic optimization problems under which closed form solutions can be found. In this note, we show that such result also holds for mean-risk-skewness portfolio optimization problems when the underlying distribution is a larger class of normal mean-variance mixture (NMVM) models than the class of AL distributions. We then study the value at risk (VaR) and conditional value at risk (CVaR) risk measures on portfolios of returns with NMVM distributions. They have closed form expressions for portfolios of normal and more generally elliptically distributed returns as discussed in Rockafellar & Uryasev (2000) and in Landsman & Valdez (2003). When the returns have general NMVM distributions, these risk measures do not give closed form expressions. In this note, we give approximate closed form expressions for VaR and CVaR of portfolios of returns with NMVM distributions. Numerical tests show that our closed form formulas give accurate values for VaR and CVaR and shortens the computational time for portfolio optimization problems associated with VaR and CVaR considerably.

q-fin.PM↗