arXiv subjects

Carlos Oliveira

Publications and source records attributed to Carlos Oliveira.

12 recordsLinked to original sources

arXiv2026

Optimal Consumption and Investment with Energy-Efficiency Adoption

Despite many decades of research, economically grounded models that analyse energy consumption and energy-efficiency adoption within a unified framework remain underdeveloped. This article addresses this gap by proposing a model of consumption, investment, and energy-efficiency adoption under uncertainty. It develops new definitions of the rebound and backfire effects, and integrates their welfare implications into a model of optimal subsidy design. Macro-level technology diffusion and energy consumption across heterogeneous agents are also formalised. Explicit results for core objects are derived, including the adoption threshold and post-adoption strategies, and these are shown to depend on agent wealth, introducing a novel channel through which financial conditions influence technology-adoption decisions. An approximation scheme is proposed to estimate welfare implications explicitly. Adoption of energy efficiency is shown to be welfare improving in the main. A detailed case study of a representative German single-family home illustrates the theoretical results. Numerical analysis indicates that the subsidy policy effectively steers aggregate energy consumption.

econ.GN↗

arXiv2023

Pathwise stochastic control and a class of stochastic partial differential equations

We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We show that the value process is the unique solution of this equation, in the viscosity sense. Finally, we discuss a version of some corresponding stochastic pathwise Noether theorem.

math.PR↗

arXiv2023

On the well-posedness of a Hamilton-Jacobi-Bellman equation with transport noise

In this paper we consider the following non-linear stochastic partial differential equation (SPDE): \begin{align*} \begin{cases} \mathrm{d}u(s,x)=\sum^n_{i=1} \mathscr{L}_i u(s,x)\circ \mathrm{d}W_i(s)+\left(V(x)+μΔu(s,x)-\frac{1}{2}\vert\nabla u(s,x)\vert^2\right)\mathrm{d}s, \quad &\text{in } (0,T)\times \mathbb{T}^n, u(0,x)=u_0(x), & \text{on } \mathbb{T}^n, \end{cases} \end{align*} where $\mathbb{T}^n$ is the $n$-dimensional torus, the functions $u_0, V: \mathbb{T}^n \to \mathbb{R}$ are given and $\{\mathscr{L}_i\}_i$ is a collection of first order linear operators. This can be seen as a Cauchy problem for a Hamilton-Jacobi-Bellman equation with transport noise in any space dimension. We introduce the concept of a strong solution from the realm of PDEs and establish the existence and uniqueness of maximal solutions (strong solutions upto a stopping time). Moreover, for a particular class of $\{\mathscr{L}_i\}_i$ we establish global well-posedness of strong solutions. The proof relies on studying an associated truncated version of the original SPDE and showing its global well-posedness in the class of strong solutions.

math.AP↗

arXiv2022

Multi-View Photometric Stereo Revisited

Multi-view photometric stereo (MVPS) is a preferred method for detailed and precise 3D acquisition of an object from images. Although popular methods for MVPS can provide outstanding results, they are often complex to execute and limited to isotropic material objects. To address such limitations, we present a simple, practical approach to MVPS, which works well for isotropic as well as other object material types such as anisotropic and glossy. The proposed approach in this paper exploits the benefit of uncertainty modeling in a deep neural network for a reliable fusion of photometric stereo (PS) and multi-view stereo (MVS) network predictions. Yet, contrary to the recently proposed state-of-the-art, we introduce neural volume rendering methodology for a trustworthy fusion of MVS and PS measurements. The advantage of introducing neural volume rendering is that it helps in the reliable modeling of objects with diverse material types, where existing MVS methods, PS methods, or both may fail. Furthermore, it allows us to work on neural 3D shape representation, which has recently shown outstanding results for many geometric processing tasks. Our suggested new loss function aims to fits the zero level set of the implicit neural function using the most certain MVS and PS network predictions coupled with weighted neural volume rendering cost. The proposed approach shows state-of-the-art results when tested extensively on several benchmark datasets.

cs.CV↗

arXiv2022

Uncertainty-Aware Deep Multi-View Photometric Stereo

This paper presents a simple and effective solution to the longstanding classical multi-view photometric stereo (MVPS) problem. It is well-known that photometric stereo (PS) is excellent at recovering high-frequency surface details, whereas multi-view stereo (MVS) can help remove the low-frequency distortion due to PS and retain the global geometry of the shape. This paper proposes an approach that can effectively utilize such complementary strengths of PS and MVS. Our key idea is to combine them suitably while considering the per-pixel uncertainty of their estimates. To this end, we estimate per-pixel surface normals and depth using an uncertainty-aware deep-PS network and deep-MVS network, respectively. Uncertainty modeling helps select reliable surface normal and depth estimates at each pixel which then act as a true representative of the dense surface geometry. At each pixel, our approach either selects or discards deep-PS and deep-MVS network prediction depending on the prediction uncertainty measure. For dense, detailed, and precise inference of the object's surface profile, we propose to learn the implicit neural shape representation via a multilayer perceptron (MLP). Our approach encourages the MLP to converge to a natural zero-level set surface using the confident prediction from deep-PS and deep-MVS networks, providing superior dense surface reconstruction. Extensive experiments on the DiLiGenT-MV benchmark dataset show that our method provides high-quality shape recovery with a much lower memory footprint while outperforming almost all of the existing approaches.

cs.CV↗

arXiv2021

Uncalibrated Neural Inverse Rendering for Photometric Stereo of General Surfaces

This paper presents an uncalibrated deep neural network framework for the photometric stereo problem. For training models to solve the problem, existing neural network-based methods either require exact light directions or ground-truth surface normals of the object or both. However, in practice, it is challenging to procure both of this information precisely, which restricts the broader adoption of photometric stereo algorithms for vision application. To bypass this difficulty, we propose an uncalibrated neural inverse rendering approach to this problem. Our method first estimates the light directions from the input images and then optimizes an image reconstruction loss to calculate the surface normals, bidirectional reflectance distribution function value, and depth. Additionally, our formulation explicitly models the concave and convex parts of a complex surface to consider the effects of interreflections in the image formation process. Extensive evaluation of the proposed method on the challenging subjects generally shows comparable or better results than the supervised and classical approaches.

cs.CV↗

arXiv2020

Time-symmetric optimal stochastic control problems in space-time domains

We present a pair of adjoint optimal control problems characterizing a class of time-symmetric stochastic processes defined on random time intervals. The associated PDEs are of free-boundary type. The particularity of our approach is that it involves two adjoint optimal stopping times adapted to a pair of filtrations, the traditional increasing one and another, decreasing. They are the keys of the time symmetry of the construction, which can be regarded as a generalization of "Schrödinger's problem" (1931-32) to space-time domains. The relation with the notion of "Hidden diffusions" is also described.

math.PR↗

arXiv2018

An Investment Model with Switching Costs and the Option to Abandon

We develop a complete analysis of a general entry-exit-scrapping model. In particular, we consider an investment project that operates within a random environment and yields a payoff rate that is a function of a stochastic economic indicator such as the price of or the demand for the project's output commodity. We assume that the investment project can operate in two modes, an "open" one and a "closed" one. The transitions from one operating mode to the other one are costly and immediate, and form a sequence of decisions made by the project's management. We also assume that the project can be permanently abandoned at a discretionary time and at a constant sunk cost. The objective of the project's management is to maximise the expected discounted payoff resulting from the project's management over all switching and abandonment strategies. We derive the explicit solution to this stochastic control problem that involves impulse control as well as discretionary stopping. It turns out that this has a rather rich structure and the optimal strategy can take eight qualitatively different forms, depending on the problems data.

math.OC↗

arXiv2018

Optimal Investment Decision Under Switching regimes of Subsidy Support

We address the problem of making a managerial decision when the investment project is subsidized, which results in the resolution of an infinite-horizon optimal stopping problem of a switching diffusion driven by either an homogeneous or an inhomogeneous continuous-time Markov chain. We provide a characterization of the value function (and optimal strategy) of the optimal stopping problem. On the one hand, broadly, we can prove that the value function is the unique viscosity solution to a system of HJB equations. On the other hand, when the Markov chain is homogeneous and the switching diffusion is one-dimensional, we obtain stronger results: the value function is the difference between two convex functions.

math.PR↗

arXiv2017

Optimal stopping of one-dimensional diffusions with integral criteria

This paper provides a full characterization of the value function and solution(s) of an optimal stopping problem for a one-dimensional diffusion with an integral criterion. The results hold under very weak assumptions, namely, the diffusion is assumed to be a weak solution of stochastic differential equation satisfying the Engelbert-Schmidt conditions, while the (stochastic) discount rate and the integrand are required to satisfy only general integrability conditions.

math.PR↗

arXiv2017

On a Class of Optimal Stopping Problems with Applications to Real Option Theory

We consider an optimal stopping time problem related with many models found in real options problems. The main goal of this work is to bring for the field of real options, different and more realistic pay-off functions, and negative interest rates. Thus, we present analytical solutions for a wide class of pay-off functions, considering quite general assumptions over the model. Also, an extensive and general sensitivity analysis to the solutions, and an economic example which highlight the mathematical difficulties in the standard approaches, are provided.

math.OC↗

arXiv2013

New Approach to Derive the Value Function of a Firm with Exit Option

In this paper we propose a new way of proving the value of a firm that is currently producing a certain product and faces the option to exit the market. The problem of optimal exiting is an optimal stopping problem, that can be solved using the dynamic programming principle. This approach leads to a partial differential equation, called the Hamilton-Jacobi-Bellman equation. This is a free-boundary problem, and therefore, we propose an approximation for the original model. We prove the convergence of the solution of the approximated problem to the original one and finally, using the Implicit Function Theorem, we obtain this solution.

math.OC↗