Estimating generation costs from observed electricity market data is essential for market simulation, strategic bidding, and system planning. To that end, we model the relationship between generation costs and production schedules with a latent variable model. Estimating generation costs from observed schedules is then formulated as Bayesian inference. A prior distribution encodes an initial belief on parameters, and the inference consists of updating the belief with the posterior distribution given observations. We use balanced neural posterior estimation (BNPE) to learn this posterior. Validation on the IEEE RTS-96 test system shows that marginal costs are recovered with narrow credible intervals, while start-up costs remain largely unidentifiable from schedules alone. The method is benchmarked against an inverse-optimization algorithm that exhibits larger parameter errors without uncertainty quantification.
We solve in semi-explicit form a class of non-Markovian stochastic optimal control problems with path-dependent rewards, using path signatures. We reformulate the control problem as the computation of Laplace transforms of signature functionals thanks to the Boué-Dupuis representation. Exploiting recent signature representations of such transforms on tensor algebras, we determine the value process and the optimal control through an infinite-dimensional system of Riccati equations on the extended tensor algebra. We establish an explicit feedback representation of the optimal control and the value process as an infinite linear combination of the time-extended signature of the controlled process, with time-dependent coefficients. The expansions being intrinsically local, we propose a dynamic recentering algorithm to ensure a global representation over the entire time horizon. We illustrate the approach on genuinely path-dependent, non-linear examples that go beyond the tractable linear-quadratic setting, including the tracking of linear functionals of the signature and signature lifts of Volterra control problems.
The global transition to renewable energy is transforming power systems, necessitating advanced transmission solutions to ensure reliability and resilience. High-voltage direct current (HVdc) systems, particularly multiterminal dc (MTdc) networks, are pivotal in integrating diverse renewable energy sources into hybrid ac/dc networks. These systems facilitate efficient power transfer over long distances and enable dynamic energy sharing across regions. However, the increasing penetration of inverter-based resources introduces complex control challenges that must be addressed to maintain grid stability and resilience.
How should policymakers mitigate investment risk in renewable electricity markets without undermining the efficiency of spot markets? Risk mitigation instruments can foster investment in financially incomplete markets but may distort operating incentives, contributing, for example, to increasingly frequent negative electricity prices. In Mitigating Market Incompleteness with Minor Market Distortions: The Case of Negative Spot Prices for Electricity, Ibrahim Abada and Andreas Ehrenmann develop a bi-level programming framework that explicitly incorporates these distortions when addressing market incompleteness. At the lower level, risk-averse agents make investment and operating decisions in an incomplete electricity market. At the upper level, a central planner optimally designs contracts for difference and price markups to maximize social welfare. The paper establishes an existence result, develops an algorithm for finding a solution, and applies the framework to a detailed numerical simulation inspired by the French power system. The results show that carefully designed risk mitigation instruments can enhance welfare while substantially limiting market distortions and the prevalence of negative prices.
We establish an infinite-dimensional affine transform theory for the time-augmented Brownian signature. Our first main result shows that, for a suitable class of linear functions of the signature, the conditional Fourier-Laplace transform admits an entire signature expansion. We prove that the associated coefficients solve an infinite-dimensional linear differential equation on the extended tensor algebra. Our second main result shows that the logarithm admits a local signature expansion whose coefficients satisfy a Riccati equation on the extended tensor algebra, revealing a generalized affine structure of the Brownian signature in a genuinely path-dependent setting. In contrast to conventional affine processes, we show that this representation is intrinsically local: zeros of the Fourier-Laplace transform in the complex plane prevent any global expansion. To recover global representations, we introduce a new class of randomized Riccati equations with path-dependent terminal conditions through a recentering argument. Furthermore, we establish uniqueness of solutions to the linear and Riccati equations within a suitable class of solutions. Our results provide a theoretical framework for transform methods in non-Markovian settings, with applications to the computation of conditional distributions.
