We present a model based on the concept of saturation for small $Q^2$ and small $x$. With only three parameters we achieve a good description of all Deep Inelastic Scattering data below $x=0.01$. This includes a consistent treatment of charm and a successful extrapolation into the photoproduction regime. The same model leads to a roughly constant ratio of diffractive and inclusive cross section.
We study whether generative AI can automate feature discovery in U.S. equities. Using large language models with retrieval-augmented generation and structured/programmatic prompting, we synthesize economically motivated features from analyst, options, and price-volume data. These features are then used as inputs to a tabular machine-learning model to forecast short-horizon returns. Across multiple datasets, AI-generated features are consistently competitive with baselines, with Sharpe improvements ranging from 14% to 91% depending on dataset and configuration. Retrieval quality is pivotal: better knowledge bases materially improve outcomes. The AI-generated signals are weakly correlated with traditional features, supporting combination. Overall, generative AI can meaningfully augment feature discovery when retrieval quality is controlled, producing interpretable signals while reducing manual engineering effort.
Eduardo Abi Jaber, Donatien Hainaut, Edouard Motte
We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an inherently nonlinear and non-Markovian stochastic control problem into a tractable form, yielding hedging strategies in (possibly infinite) linear feedback form in the time-augmented signature of the control variables, with coefficients characterized by non-standard infinite-dimensional Riccati equations on the extended tensor algebra. Numerical experiments demonstrate the effectiveness of these signature-based strategies for pricing and hedging general path-dependent payoffs in the presence of frictions. In particular, market impact naturally smooths optimal trading strategies, making low-truncated signature approximations highly accurate and robust in frictional markets, contrary to the frictionless case.
Decision-theoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In single-agent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Q-value functions: an optimal Q-value function Q* is computed in a recursive manner by dynamic programming, and then an optimal policy is extracted from Q*. In this paper we study whether similar Q-value functions can be defined for decentralized POMDP models (Dec-POMDPs), and how policies can be extracted from such value functions. We define two forms of the optimal Q-value function for Dec-POMDPs: one that gives a normative description as the Q-value function of an optimal pure joint policy and another one that is sequentially rational and thus gives a recipe for computation. This computation, however, is infeasible for all but the smallest problems. Therefore, we analyze various approximate Q-value functions that allow for efficient computation. We describe how they relate, and we prove that they all provide an upper bound to the optimal Q-value function Q*. Finally, unifying some previous approaches for solving Dec-POMDPs, we describe a family of algorithms for extracting policies from such Q-value functions, and perform an experimental evaluation on existing test problems, including a new firefighting benchmark problem.
The paper discusses capital allocation using the Euler formula and focuses on the risk measures Value-at-Risk (VaR) and Expected shortfall (ES). Some new results connected to this capital allocation is known. Two examples illustrate that capital allocation with VaR is not monotonous which may be surprising since VaR is monotonous. A third example illustrates why the same risk measure should be used in capital allocation as in the evaluation of the total portfolio. We show how simulation may be used in order to estimate the expected Return on risk adjusted capital in the commitment period of an asset. Finally, we show how Markov chain Monte Carlo may be used in the estimation of the capital allocation.
A bstractWe introduce a new framework for constructing black hole solutions that are holographically dual to strongly coupled field theories with explicitly broken translation invariance. Using a classical gravitational theory with a continuous global symmetry leads to constructions that involve solving ODEs instead of PDEs. We study in detail D = 4 Einstein-Maxwell theory coupled to a complex scalar field with a simple mass term. We construct black holes dual to metallic phases which exhibit a Drude-type peak in the optical conductivity, but there is no evidence of an intermediate scaling that has been reported in other holographic lattice constructions. We also construct black holes dual to insulating phases which exhibit a suppression of spectral weight at low frequencies. We show that the model also admits a novel AdS3 × $ \mathbb{R} $ solution.
This paper addresses the importance of incorporating various risk measures in portfolio management and proposes a dynamic hybrid portfolio optimization model that combines the spectral risk measure and the Value-at-Risk in the mean-variance formulation. By utilizing the quantile optimization technique and martingale representation, we offer a solution framework for these issues and also develop a closed-form portfolio policy when all market parameters are deterministic. Our hybrid model outperforms the classical continuous-time mean-variance portfolio policy by allocating a higher position of the risky asset in favorable market states and a less risky asset in unfavorable market states. This desirable property leads to promising numerical experiment results, including improved Sortino ratio and reduced downside risk compared to the benchmark models.
The problem of adaptive traffic signal control in the multi-intersection system has attracted the attention of researchers. Among the existing methods, reinforcement learning has shown to be effective. However, the complex intersection features, heterogeneous intersection structures, and dynamic coordination for multiple intersections pose challenges for reinforcement learning-based algorithms. This paper proposes a cooperative deep Q-network with Q-value transfer (QT-CDQN) for adaptive multi-intersection signal control. In QT-CDQN, a multi-intersection traffic network in a region is modeled as a multi-agent reinforcement learning system. Each agent searches the optimal strategy to control an intersection by a deep Q-network that takes the discrete state encoding of traffic information as the network inputs. To work cooperatively, the agent considers the influence of the latest actions of its adjacencies in the process of policy learning. Especially, the optimal Q-values of the neighbor agents at the latest time step are transferred to the loss function of the Q-network. Moreover, the strategy of the target network and the mechanism of experience replay are used to improve the stability of the algorithm. The advantages of QT-CDQN lie not only in the effectiveness and scalability for the multi-intersection system but also in the versatility to deal with the heterogeneous intersection structures. The experimental studies under different road structures show that the QT-CDQN is competitive in terms of average queue length, average speed, and average waiting time when compared with the state-of-the-art algorithms. Furthermore, the experiments of recurring congestion and occasional congestion validate the adaptability of the QT-CDQN to dynamic traffic environments.
We establish a $q$-analogue of Sun--Zhao's congruence on harmonic sums. Based on this $q$-congruence and a $q$-series identity, we prove a congruence conjecture on sums of central $q$-binomial coefficients, which was recently proposed by Guo. We also deduce a $q$-analogue of a congruence due to Apagodu and Zeilberger from Guo's $q$-congruence.
This paper studies the topic of cost-efficiency in incomplete markets. A payoff is called cost-efficient if it achieves a given probability distribution at some given investment horizon with a minimum initial budget. Extensive literature exists for the case of a complete financial market. We show how the problem can be extended to incomplete markets and how the main results from the theory of complete markets still hold in adapted form. In particular, we find that in incomplete markets, the optimal portfolio choice for non-decreasing preferences that are diversification-loving (a notion introduced in this paper) must be "perfectly" cost-efficient. This notion of perfect cost-efficiency is shown to be equivalent to the fact that the payoff can be rationalized, i.e., it is the solution to an expected utility problem.