Search Results (50)

This paper introduces a novel multi-objective optimization framework for sustainable portfolio rebalancing under uncertainty. The model simultaneously targets return maximization, downside risk control, and liquidity preservation, addressing the complex trade-offs faced by investors in volatile markets. Unlike traditional static approaches, the framework allows for dynamic asset reallocation and explicitly incorporates nonlinear transaction costs, offering a more realistic representation of trading frictions. Key financial parameters—including expected returns, volatility, and liquidity—are modeled using interval arithmetic, enabling a flexible, distribution-free depiction of uncertainty. Risk is measured through semi-absolute deviation, providing a more intuitive and robust assessment of downside exposure compared to classical variance. A core innovation lies in the behavioral modeling of investor preferences, operationalized through three strategic configurations, pessimistic, optimistic, and mixed, implemented via convex combinations of interval bounds. The framework is empirically validated using a diversified cryptocurrency portfolio consisting of Bitcoin, Ethereum, Solana, and Binance Coin, observed over a six-month period. The simulation results confirm the model’s adaptability to shifting market conditions and investor sentiment, consistently generating stable and diversified allocations. Beyond its technical rigor, the proposed framework aligns with sustainability principles by enhancing portfolio resilience, minimizing systemic concentration risks, and supporting long-term decision-making in uncertain financial environments. Its integrated design makes it particularly suitable for modern asset management contexts that require flexibility, robustness, and alignment with responsible investment practices. Full article

In direct-current gas-insulated transmission lines (DC GIL), complex heat transfer processes accelerate surface charge accumulation on insulators, causing local electric field distortion and elevating the risk of surface flashover. This study develops a three-dimensional multi-physics coupled mathematical model for ±200 kV DC GIL basin-type insulators. The bulk and surface conductivity of insulator materials were experimentally measured under varying temperature and electric field conditions, with fitting equations derived to describe their behavior. The model investigates surface charge accumulation and electric field distribution under DC voltage and polarity-reversal conditions, incorporating multi-field coupling effects. Results show that, at a 3150 A current in a horizontally arranged DC GIL, insulator temperatures reach approximately 62.8 °C near the conductor and 32 °C near the enclosure, with the convex surface exhibiting higher temperatures than the concave surface and distinct radial variations. Under DC voltage, surface charge accumulates faster in high-temperature regions, with both charge and electric field distributions stabilizing after approximately 300 h, following significant changes within the first 40 h. Following stabilization, the distribution of surface charge and electric field varies across different radial directions. During polarity reversal, residual surface charges cause electric field distortion, increasing maximum field strength by 13.6% and 47.2% on the convex and concave surfaces, respectively, with greater distortion on the concave surface, as calculated from finite element simulations with a numerical accuracy of ±0.5% based on mesh convergence and solver tolerance. These findings offer valuable insights for enhancing DC GIL insulation performance. Full article

This paper demonstrates that perfectly calibrating a multi-asset model to observed market prices of all basket call options is insufficient to uniquely determine the price of a best-of call option. Previous research on multi-asset option pricing has primarily focused on complete market settings or assumed specific parametric models, leaving fundamental questions about model risk and pricing uniqueness in incomplete markets inadequately addressed. This limitation has critical practical implications: derivatives practitioners who hedge best-of options using basket-equivalent instruments face fundamental distributional uncertainty that compounds the well-recognized non-linearity challenges. We establish this non-uniqueness using convex analysis (extreme ray characterization demonstrating geometric incompatibility between payoff structures), measure theory (explicit construction of distinct equivalent probability measures), and geometric analysis (payoff structure comparison). Specifically, we prove that the set of equivalent probability measures consistent with observed basket prices contains distinct measures yielding different best-of option prices, with explicit no-arbitrage bounds $[a_K,b_K]$ quantifying this uncertainty. Our theoretical contribution provides the first rigorous mathematical foundation for several empirically observed market phenomena: wide bid-ask spreads on extremal options, practitioners’ preference for over-hedging strategies, and substantial model reserves for exotic derivatives. We demonstrate through concrete examples that substantial model risk persists even with perfect basket calibration and equivalent measure constraints. For risk-neutral pricing applications, equivalent martingale measure constraints can be imposed using optimal transport theory, though this requires additional mathematical complexity via Schrödinger bridge techniques while preserving our fundamental non-uniqueness results. The findings establish that additional market instruments beyond basket options are mathematically necessary for robust exotic derivative pricing. Full article

The risk measures such as value at risk, and conditional values at risk do not always account for the sensitivity of large losses with certainty, as large losses often break the homogeneity especially seen in an illiquidity risk. In this study, we examine the characteristics of large-loss sensitivity more holistically, including small probability, within the framework of risk measures. The analysis incorporates the certainty equivalent, generation of the optimal certainty equivalent formulation, divergence utility, and general utility functions in their original form, and their relationship with expectiles and elicitability. The discussion provides a summary in the understanding of risk measure status and sensitivity involving small probably cases. Additionally, we evaluate large-loss sensitivity in risk-sharing scenarios using the convex conjugation of the divergence utility. By clarifying the conditions affecting large-loss sensitivity, the findings highlight the limitations of existing risk measures and suggest directions for future improvement. Furthermore, these insights contribute to enhancing the stability of risk-sharing business models. Full article

This paper examines the extent of stock-returns’ co-movements among firms in different countries and explores how various measures of closeness affect those co-movements by estimating a spatial autoregressive (SAR) convex combination model that merges four weight matrices—geographical distance, bilateral trade, sector similarity, and company size—into one global matrix. Our results reveal strong spatial stock-market dependence, show that spatial proximity is better captured by financial-distance measures than by pure geographical distance, and indicate that the weight matrix based on sector similarities outperforms the other linkages in explaining firms’ co-movements. Extending the traditional SAR model, the study simultaneously evaluated cross-country and within-country dependencies, providing insights valuable to investors building optimal portfolios and to policymakers monitoring contagion and systemic risk. Full article

In this paper, we take a new perspective to describe the model uncertainty, and thus propose two new classes of risk measures under model uncertainty. To be precise, we use an auxiliary random variable to describe model uncertainty. By proposing new sets of axioms under model uncertainty, we axiomatically introduce and characterize conditional coherent and convex risk measures under a random environment, respectively. As examples, we also discuss the connections of the introduced conditional coherent risk measures under random environments with two existing risk measures. This paper mainly gives some theoretical results, and it is expected to make meaningful complement to the study of coherent and convex risk measures under model uncertainty. Full article

We introduce a new coherent risk measure, the minimal-entropy risk measure, which is built on the minimal-entropy $\sigma$-martingale measure—a concept inspired by the well-known minimal-entropy martingale measure used in option pricing. While the minimal-entropy martingale measure is commonly used for pricing and hedging, the minimal-entropy $\sigma$-martingale measure has not previously been studied, nor has it been analyzed as a traditional risk measure. We address this gap by clearly defining this new risk measure and examining its fundamental properties. In addition, we revisit the entropic risk measure, typically expressed through an exponential formula. We provide an alternative definition using a supremum over Kullback–Leibler divergences, making its connection to entropy clearer. We verify important properties of both risk measures, such as convexity and coherence, and extend these concepts to dynamic situations. We also illustrate their behavior in scenarios involving optimal risk transfer. Our results link entropic concepts with incomplete-market pricing and demonstrate how both risk measures share a unified entropy-based foundation. Full article

In this paper, we focus on capital allocation methods based on marginal contributions. In particular, concerning the relation between linear capital allocation rules and the well-known Gradient (or Euler) allocation, we investigate an extension to the convex and non-differentiable case of the result above and its link with the “generalized collapse to the mean” problem. This preliminary result goes in the direction of applying the popular marginal contribution method, which fosters the diversification of risk, to the case of more general risk measures. In this context, we will also discuss and point out some numerical issues linked to marginal methods and some future research directions. Full article

Multi-station radar can provide better performance against deception jamming, but the harsh detection requirements and risk of network destruction undermine the practicability of the multi-station radar. Therefore, it is necessary to further explore the anti-deception jamming performance of a single-station radar. This paper introduces a novel method, based on parameter estimation with a virtual multi-station system, to discriminate range deceptive jamming. The system consists of a single-station radar assisted by the reconfigurable intelligent surfaces (RIS). A unified parameter estimation model for true and false targets is established, and the convex optimization method is applied to estimate the target location and deception range. The Cramer–Rao lower bound (CRLB) of the target localization and the measured deception range is then derived. By using the measured deception range and its CRLB, an optimal discrimination algorithm in accordance with the Neyman–Pearson lemma is designed. Simulation results demonstrate the feasibility of the proposed method and analyze the effects of factors such as signal-to-noise ratio (SNR), deception range, jammer location, and the RISs station arrangement on the discrimination performance. Full article

This study refines the methodology for solving stochastic optimal control problems with quality criteria that include the sum of the quality functional of the classical formulation and an extremal measure. A two-level optimization solution of these kinds of problems is presented already for the case where the quality functional consists only of the extremal measure. Our study shows the possibility of solving the original time inconsistency problem through solving a two-level optimization problem, where the outer problem is solved by gradient methods since the value function is convex and the inner problem is solved by classical methods. Some experiments were carried out and confirmed the validity of the theory. The results of the study can be applied to the case of portfolio management with quality criteria containing the Conditional Value-at-Risk (CVaR) metric. Full article

This survey offers a succinct overview of the General Framework of Portfolio Theory (GFPT), consolidating Markowitz portfolio theory, the growth optimal portfolio theory, and the theory of risk measures. Central to this framework is the use of convex analysis and duality, reflecting the concavity of reward functions and the convexity of risk measures due to diversification effects. Furthermore, practical considerations, such as managing multiple risks in bank balance sheets, have expanded the theory to encompass vector risk analysis. The goal of this survey is to provide readers with a concise tour of the GFPT’s key concepts and practical applications without delving into excessive technicalities. Instead, it directs interested readers to the comprehensive monograph of Maier-Paape, Júdice, Platen, and Zhu (2023) for detailed proofs and further exploration. Full article

This paper considers the impact of the composition of the top management team on the credit default risk of the firm. Finance theory suggests that shareholders prefer higher levels of risk than the risk-averse executives managing the firm. Increasing the influence of female executives may reduce credit default risk, as female executives have been shown to be associated with lower firm risk. Alternatively, as diversity has been shown to improve the quality of group decision-making, a higher but optimal credit default risk may result. This paper uses a matched sample of 6,652 firm-year observations of publicly traded American firms over the period 2010–2020 to investigate the relationship between gender power within the top management team and credit default risk as measured by the Altman Z-score. This paper finds a convex relationship between the Altman Z-score and the influence of female executives. In other words, top management teams where power is shared between female and male executives accept higher levels of credit default risk than teams dominated by just female (or just male) executives. However, this paper also finds that an excessively high credit risk is negatively associated with the influence of female executives. Full article

In this paper, we propose a new class of systemic risk measures, which we refer to as strong comonotonic additive systemic risk measures. First, we introduce the notion of strong comonotonic additive systemic risk measures by proposing new axioms. Second, we establish a structural decomposition for strong comonotonic additive systemic risk measures. Third, when both the single-firm risk measure and the aggregation function in the structural decomposition are convex, we also provide a dual representation for it. Last, examples are given to illustrate the proposed systemic risk measures. Comparisons with existing systemic risk measures are also provided. Full article

The aim of this paper is to provide a dual representation of convex and coherent risk measures in partially ordered linear spaces with respect to the algebraic dual space. An algebraic robust representation is deduced by weak separation of convex sets by functionals, which are assumed to be only linear; thus, our framework does not require any topological structure of the underlying spaces, and our robust representations are found without any continuity requirement for the risk measures. We also use such extensions to the representation of acceptability indices. Full article

The objective is to study the use of non-translation invariant risk measures within the equal risk pricing (ERP) methodology for the valuation of financial derivatives. The ability to move beyond the class of convex risk measures considered in several prior studies provides more flexibility within the pricing scheme. In particular, suitable choices for the risk measure embedded in the ERP framework, such as the semi-mean-square-error (SMSE), are shown herein to alleviate the price inflation phenomenon observed under the tail value at risk-based ERP as documented in previous work. The numerical implementation of non-translation invariant ERP is performed through deep reinforcement learning, where a slight modification is applied to the conventional deep hedging training algorithm so as to enable obtaining a price through a single training run for the two neural networks associated with the respective long and short hedging strategies. The accuracy of the neural network training procedure is shown in simulation experiments not to be materially impacted by such modification of the training algorithm. Full article