TY - GEN A1 - Sass, Jörn A1 - Westphal, Dorothee A1 - Wunderlich, Ralf T1 - Diffusion Approximations for Expert Opinions in a Financial Market with Gaussian Drift T2 - arXiv.org Y1 - 2018 UR - https://arxiv.org/abs/1807.00568 ER - TY - GEN A1 - Redeker, Imke A1 - Wunderlich, Ralf T1 - Credit risk with asymmetric information and a switching default threshold T2 - arXiv Y1 - 2019 UR - https://arxiv.org/abs/1910.14413v2 ER - TY - GEN A1 - Gabih, Abdelali A1 - Kondakji, Hakam A1 - Wunderlich, Ralf T1 - Asymptotic filter behavior for high-frequency expert opinions in a market with Gaussian drift, Stochastic Models T2 - Stochastic Models Y1 - 2020 U6 - https://doi.org/10.1080/15326349.2020.1758567 SN - 1532-6349 VL - 36 IS - 4 SP - 519 EP - 547 ER - TY - GEN A1 - Mastroeni, Loretta A1 - Wunderlich, Ralf T1 - Introduction to Special Issue on Energy Finance T2 - Decisions in Economics and Finance Y1 - 2021 U6 - https://doi.org/10.1007/s10203-021-00367-2 SN - 1129-6569 VL - 44 IS - 2 SP - 1015 EP - 1020 ER - TY - GEN A1 - Sass, Jörn A1 - Westphal, Dorothee A1 - Wunderlich, Ralf T1 - Diffusion approximations for randomly arriving expert opinions in a financial market with Gaussian drift T2 - Journal of Applied Probability Y1 - 2021 U6 - https://doi.org/10.1017/jpr.2020.82 SN - 1475-6072 SN - 0021-9002 VL - 58 IS - 1 SP - 197 EP - 216 ER - TY - GEN A1 - Takam, Paul Honoré A1 - Wunderlich, Ralf A1 - Menoukeu Pamen, Olivier T1 - Short-Term Behavior of a Geothermal Energy Storage: Modeling and Theoretical Results T2 - arXiv.org Y1 - 2021 UR - https://arxiv.org/pdf/2104.05005.pdf SP - 1 EP - 25 ER - TY - GEN A1 - Takam, Paul Honoré A1 - Wunderlich, Ralf A1 - Menoukeu Pamen, Olivier T1 - Short-Term Behavior of a Geothermal Energy Storage: Numerical Applications T2 - arXiv.org Y1 - 2021 UR - https://arxiv.org/pdf/2104.05116.pdf SP - 1 EP - 28 ER - TY - GEN A1 - Sass, Jörn A1 - Westphal, Dorothee A1 - Wunderlich, Ralf T1 - Diffusion approximations for periodically arriving expert opinions in a financial market with Gaussian drift T2 - Stochastic Models Y1 - 2022 U6 - https://doi.org/10.1080/15326349.2022.2100423 SN - 1532-4214 VL - 39 SP - 323 EP - 362 ER - TY - GEN A1 - Takam, Paul Honoré A1 - Wunderlich, Ralf T1 - On the Input-Output Behavior of a Geothermal Energy Storage: Approximations by Model Order Reduction T2 - arXiv Y1 - 2022 U6 - https://doi.org/10.48550/arXiv.2209.14761 SP - 1 EP - 42 ER - TY - GEN A1 - Gabih, Abdelali A1 - Kondakji, Hakam A1 - Wunderlich, Ralf T1 - Well Posedness of Utility Maximization Problems Under Partial Information in a Market with Gaussian Drift T2 - arXiv Y1 - 2022 U6 - https://doi.org/10.48550/arXiv.2205.08614 SP - 1 EP - 17 ER - TY - GEN A1 - Takam, Paul Honoré A1 - Wunderlich, Ralf A1 - Menoukeu Pamen, Olivier T1 - Modeling and simulation of the input–output behavior of a geothermal energy storage T2 - Mathematical Methods in the Applied Sciences Y1 - 2024 U6 - https://doi.org/10.1002/mma.9661 SN - 0170-4214 SN - 1099-1476 VL - 47 IS - 1 SP - 371 EP - 396 ER - TY - GEN A1 - Lamert, Kerstin A1 - Auer, Benjamin R. A1 - Wunderlich, Ralf T1 - Discretization of continuous-time arbitrage strategies in financial markets with fractional Brownian motion T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2311.15635 SP - 1 EP - 32 ER - TY - GEN A1 - Gabih, Abdelali A1 - Kondakji, Hakam A1 - Wunderlich, Ralf T1 - Power Utility Maximization with Expert Opinions at Fixed Arrival Times in a Market with Hidden Gaussian Drift T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2301.06847 SP - 1 EP - 33 ER - TY - GEN A1 - Takam, Paul Honore A1 - Wunderlich, Ralf T1 - Model order reduction for the input–output behavior of a geothermal energy storage T2 - Journal of Engineering Mathematics Y1 - 2024 U6 - https://doi.org/10.1007/s10665-024-10398-4 SN - 0022-0833 VL - 148 IS - 1 SP - 1 EP - 34 PB - Springer Science and Business Media LLC ER - TY - GEN A1 - Gabih, Abdelali A1 - Kondakji, Hakam A1 - Wunderlich, Ralf T1 - Power utility maximization with expert opinions at fixed arrival times in a market with hidden Gaussian drift T2 - Annals of Operations Research Y1 - 2024 U6 - https://doi.org/10.1007/s10479-024-06172-5 SN - 0254-5330 VL - 341 IS - 2-3 SP - 897 EP - 936 PB - Springer Science and Business Media LLC ER - TY - GEN A1 - Takam, Paul Honore A1 - Wunderlich, Ralf T1 - Numerical simulation of the input-output behavior of a geothermal energy storage T2 - Energies N2 - This paper studies numerical simulations of the input-output behavior of a geothermal energy storage used in residential heating systems. There, under or aside of a building a certain domain is filled with soil and insulated from the surrounding ground. Thermal energy is stored by raising the temperature of the soil inside the storage, and pipe heat exchangers filled with a moving fluid are used to charge and discharge the storage. Numerical simulations are required for the design, operation and optimal management of heating systems that are equipped with such a thermal storage system. They help to understand the storage response to charging and discharging processes, which depend crucially on the dynamics of the spatial temperature distribution in the storage medium. The latter is modeled mathematically by an initial boundary value problem for a linear heat equation with convection. The problem is solved numerically by finite difference discretization. Finally, the results of computer simulations are presented, which show the properties of the temperature distribution in the storage and its aggregated characteristics. Y1 - 2025 U6 - https://doi.org/10.3390/en18061558 SN - 1996-1073 VL - 18 IS - 6 SP - 1558 PB - MDPI AG ER - TY - GEN A1 - Ouabo Kamkumo, Florent A1 - Mbouandi Njiasse, Ibrahim A1 - Wunderlich, Ralf T1 - Stochastic epidemic models with partial information T2 - arXiv N2 - Mathematical models of epidemics often use compartmental models dividing the population into several compartments. Based on a microscopic setting describing the temporal evolution of the subpopulation sizes in the compartments by stochastic counting processes one can derive macroscopic models for large populations describing the average behavior by associated ordinary differential equations such as the celebrated SIR model. Further, diffusion approximations allow to address fluctuations from the average and to describe the state dynamics also for smaller populations by stochastic differential equations. In general, not all state variables are directly observable, and we face the so-called "dark figure" problem, which concerns, for example, the unknown number of asymptomatic and undetected infections. The present study addresses this problem by developing stochastic epidemic models that incorporate partial information about the current state of the epidemic, also known as nowcast uncertainty. Examples include a simple extension of the SIR model, a model for a disease with lifelong immunity after infection or vaccination, and a Covid-19 model. For the latter, we propose a ``cascade state approach'' that allows to exploit the information contained in formally hidden compartments with observable inflow but unobservable outflow. Furthermore, parameter estimation and calibration are performed using ridge regression for the Covid-19 model. The results of the numerical simulations illustrate the theoretical findings. Y1 - 2025 U6 - https://doi.org/10.48550/arXiv.2503.07251 SP - 1 EP - 55 ER - TY - GEN A1 - Mbouandi Njiasse, Ibrahim A1 - Ouabo Kamkumo, Florent A1 - Wunderlich, Ralf T1 - Stochastic optimal control of an epidemic under partial information T2 - arXiv N2 - In this paper, we address a social planner's optimal control problem for a partially observable stochastic epidemic model. The control measures include social distancing, testing, and vaccination. Using a diffusion approximation for the state dynamics of the epidemic, we apply filtering arguments to transform the partially observable stochastic optimal control problem into an optimal control problem with complete information. This transformed problem is treated as a Markov decision process. The associated Bellman equation is solved numerically using optimal quantization methods for approximating the expectations involved to mitigate the curse of dimensionality. We implement two approaches, the first involves state discretization coupled with linear interpolation of the value function at non-grid points. The second utilizes a parametrization of the value function with educated ansatz functions. Extensive numerical experiments are presented to demonstrate the efficacy of both methods. Y1 - 2025 U6 - https://doi.org/10.48550/arXiv.2503.06804 SP - 1 EP - 52 ER - TY - GEN A1 - Takam, Paul Honoré A1 - Wunderlich, Ralf T1 - Cost-optimal management of a residential heating system with a geothermal energy storage under uncertainty T2 - arXiv Y1 - 2025 U6 - https://doi.org/10.48550/arXiv.2502.19619 SP - 1 EP - 41 ER - TY - GEN A1 - Pilling, Eric A1 - Bähr, Martin A1 - Wunderlich, Ralf T1 - Stochastic optimal control of an industrial Power-to-Heat System with high-temperature heat pump and thermal energy storage T2 - arXiv N2 - The optimal control of sustainable energy supply systems, including renewable energies and energy storage, takes a central role in the decarbonization of industrial systems. However, the use of fluctuating renewable energies leads to fluctuations in energy generation and requires a suitable control strategy for the complex systems in order to ensure energy supply. In this paper, we consider an electrified power-to-heat system which is designed to supply heat in form of superheated steam for industrial processes. The system consists of a high-temperature heat pump for heat supply, a wind turbine for power generation, a sensible thermal energy storage for storing excess heat and a steam generator for providing steam. If the system's energy demand cannot be covered by electricity from the wind turbine, additional electricity must be purchased from the power grid. For this system, we investigate the cost-optimal operation aiming to minimize the electricity cost from the grid by a suitable system control depending on the available wind power and the amount of stored thermal energy. This is a decision making problem under uncertainties about the future prices for electricity from the grid and the future generation of wind power. The resulting stochastic optimal control problem is treated as finite-horizon Markov decision process for a multi-dimensional controlled state process. We first consider the classical backward recursion techniques for solving the associated dynamic programming equation for the value function and compute the optimal decision rule. Since that approach suffers from the curse of dimensionality we also apply Q-learning techniques that are able to provide a good approximate solution to the optimization problem within reasonable time. Y1 - 2025 U6 - https://doi.org/10.48550/arXiv.2411.02211 SP - 1 EP - 63 ER - TY - GEN A1 - Lamert, Kerstin A1 - Auer, Benjamin R. A1 - Wunderlich, Ralf T1 - Discretization of continuous-time arbitrage strategies in financial markets with fractional Brownian motion T2 - Mathematical Methods of Operations Research Y1 - 2025 U6 - https://doi.org/10.1007/s00186-025-00889-0 SN - 1432-2994 VL - 2025 PB - Springer Science and Business Media LLC ER - TY - GEN A1 - Gabih, Abdelali A1 - Wunderlich, Ralf T1 - Portfolio optimization in a market with hidden Gaussian drift and randomly arriving expert opinions T2 - Annals of operations research N2 - This paper investigates the optimal selection of portfolios for power utility maximizing investors in a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current state of the drift arriving randomly over time. The arrival dates are modeled as the jump times of a homogeneous Poisson process. Applying Kalman filter techniques we derive estimates of the hidden drift which are described by the conditional mean and covariance of the drift given the observations. The utility maximization problem is solved with dynamic programming methods. The associated dynamic programming equation is a partial integro-differential equation and degenerate in the diffusion part of the differential operator. We therefore adopt a regularization approach and add a Brownian perturbation to the state process, scaled by a small parameter that approaches zero. We prove that the value functions of the regularized problems converge to the value function of the original problem. This enables the construction of -optimal strategies. KW - Power utility maximization KW - Partial information KW - Dynamic programming equation KW - Kalman–Bucy filter KW - Expert opinions KW - Black–Litterman model KW - Regularization Y1 - 2025 U6 - https://doi.org/10.1007/s10479-025-06796-1 SN - 1572-9338 VL - 2025 SP - 1 EP - 33 PB - Springer CY - Dordrecht ER - TY - GEN A1 - Mbouandi Njiasse, Ibrahim A1 - Ouabo Kamkumo, Florent A1 - Wunderlich, Ralf T1 - Convergence of the extended Kalman filter with small and state-dependent noise N2 - Nonlinear filtering problems are encountered in many applications, and one solution approach is the extended Kalman filter, which is not always convergent. Therefore, it is crucial to identify conditions under which the extended Kalman filter provides accurate approximations. This paper generalizes two significant results from Picard (1991) on the efficiency of the continuous-time extended Kalman filter to a more general setting where the observation noise may be state-dependent but does not allow signal reconstruction from the quadratic variation of the observation process as in epidemic models. Firstly, we show that when the observation's drift coefficient is strongly injective and the signal's and observation's drift become nearly linear for the diffusion scaling coefficient , the estimation error is of order . Subsequently, we establish conditions under which the impact of the initial filtering error decays exponentially fast. Y1 - 2025 U6 - https://doi.org/10.48550/arXiv.2511.10814 SP - 1 EP - 21 PB - arXiv CY - Ithaca, NY ER - TY - GEN A1 - Achola Oluoch, Lillian A1 - Ouabo Kamkumo, Florent A1 - Wunderlich, Ralf T1 - Stochastic models and estimation of undetected infections in the transmission of Zika virus N2 - Zika fever, a mosquito-borne viral disease with potential severe neurological complications and birth defects, remains a significant public health concern. The epidemiological models often oversimplify the dynamics of Zika transmission by assuming immediate detection of all infected cases. This study provides an enhanced SEIR (Susceptible-Exposed-Infectious-Recovered) model to incorporate partial information by distinguishing between detected and undetected Zika infections (also known as "dark figures"). By distinguishing the compartments, the model captures the complexities of disease spread by accounting for uncertainties about transmission and the number of undetected infections. This model implements the Kalman filter technique to estimate the hidden states from the observed states. Numerical simulations were performed to understand the dynamics of Zika transmission and real-world data was utilized for parameterization and validation of the model. The study aims to provide information on the impact of undetected Zika infections on disease spread within the population, which will contribute to evidence-based decision making in public health policy and practice. Y1 - 2025 U6 - https://doi.org/10.48550/arXiv.2511.01920 SP - 1 EP - 49 PB - arXiv CY - Ithaca, NY ER - TY - GEN A1 - Ouabo Kamkumo, Florent A1 - Mbouandi Njiasse, Ibrahim A1 - Wunderlich, Ralf T1 - Estimating unobservable states in stochastic epidemic models with partial information N2 - This article investigates stochastic epidemic models with partial information and addresses the estimation of current values of not directly observable states. The latter is also called nowcasting and related to the so-called "dark figure" problem, which concerns, for example, the estimation of unknown numbers of asymptomatic and undetected infections. The study is based on Ouabo Kamkumo et al. (2025), which provides detailed information about stochastic multi-compartment epidemic models with partial information and various examples. Starting point is a description of the state dynamics by a system of nonlinear stochastic recursions resulting from a time-discretization of a diffusion approximation of the underlying counting processes. The state vector is decomposed into an observable and an unobservable component. The latter is estimated from the observations using the extended Kalman filter approach in order to take into account the nonlinearity of the state dynamics. Numerical simulations for a Covid-19 model with partial information are presented to verify the performance and accuracy of the estimation method. Y1 - 2025 U6 - https://doi.org/10.48550/arXiv.2506.00906 SP - 1 EP - 32 PB - arXiv CY - Ithaca, NY ER -