@misc{FreyGabihWunderlich, author = {Frey, R{\"u}diger and Gabih, Abdelali and Wunderlich, Ralf}, title = {Portfolio optimization under partial information with expert opinions}, series = {International Journal of Theoretical and Applied Finance}, volume = {15}, journal = {International Journal of Theoretical and Applied Finance}, number = {1}, doi = {10.1142/S0219024911006486}, pages = {1250009-1 -- 1250009-17}, language = {en} } @misc{FreyWunderlich, author = {Frey, R{\"u}diger and Wunderlich, Ralf}, title = {Dynamic Programming Equations for Portfolio Optimization under Partial Information with Expert Opinions}, series = {ArXiv.org}, journal = {ArXiv.org}, pages = {31}, language = {en} } @misc{FreyGabihWunderlich, author = {Frey, R{\"u}diger and Gabih, Abdelali and Wunderlich, Ralf}, title = {Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach}, series = {Communications on Stochastic Analysis}, volume = {8}, journal = {Communications on Stochastic Analysis}, number = {1}, issn = {0973-9599}, pages = {49 -- 79}, language = {en} } @misc{GabihKondakjiSassetal., author = {Gabih, Abdelali and Kondakji, Hakam and Sass, J{\"o}rn and Wunderlich, Ralf}, title = {Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift}, series = {Communications on Stochastic Analysis}, volume = {8}, journal = {Communications on Stochastic Analysis}, number = {1}, issn = {0973-9599}, pages = {27 -- 47}, language = {en} } @misc{HoefersWunderlich, author = {H{\"o}fers, Imke and Wunderlich, Ralf}, title = {Portfolio optimization under dynamic risk constraints}, series = {arXiv.org}, journal = {arXiv.org}, pages = {28}, language = {en} } @misc{SassWestphalWunderlich, author = {Sass, J{\"o}rn and Westphal, Dorothee and Wunderlich, Ralf}, title = {Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift}, series = {ArXiv.org}, journal = {ArXiv.org}, pages = {30}, language = {en} } @misc{ShardinWunderlich, author = {Shardin, Anton and Wunderlich, Ralf}, title = {Partially Observable Stochastic Optimal Control Problems for an Energy Storage}, series = {Stochastics : an International Journal of Probability and Stochastic Processes}, volume = {89}, journal = {Stochastics : an International Journal of Probability and Stochastic Processes}, number = {1}, issn = {1744-2516}, pages = {280 -- 310}, language = {en} } @misc{RedekerWunderlich, author = {Redeker, Imke and Wunderlich, Ralf}, title = {Portfolio optimization under dynamic risk constraints: Continuous vs. discrete time trading}, series = {Statistics \& Risk Modeling}, volume = {35}, journal = {Statistics \& Risk Modeling}, number = {1-2}, issn = {2196-7040}, doi = {10.1515/strm-2017-0001}, pages = {1 -- 21}, language = {en} } @misc{SassWestphalWunderlich, author = {Sass, J{\"o}rn and Westphal, Dorothee and Wunderlich, Ralf}, title = {Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift}, series = {International Journal of Theoretical and Applied Finance}, volume = {20}, journal = {International Journal of Theoretical and Applied Finance}, number = {4}, issn = {0219-0249}, doi = {10.1142/S0219024917500224}, pages = {1750022}, language = {en} } @misc{GabihKondakjiWunderlich, author = {Gabih, Abdelali and Kondakji, Hakam and Wunderlich, Ralf}, title = {Asymptotic Filter Behavior for High-Frequency Expert Opinions in a Market with Gaussian Drift}, series = {arXiv.org}, journal = {arXiv.org}, pages = {17}, language = {en} } @misc{SassWestphalWunderlich, author = {Sass, J{\"o}rn and Westphal, Dorothee and Wunderlich, Ralf}, title = {Diffusion Approximations for Expert Opinions in a Financial Market with Gaussian Drift}, series = {arXiv.org}, journal = {arXiv.org}, pages = {42}, language = {en} } @misc{RedekerWunderlich, author = {Redeker, Imke and Wunderlich, Ralf}, title = {Credit risk with asymmetric information and a switching default threshold}, series = {arXiv}, journal = {arXiv}, pages = {20}, language = {en} } @misc{GabihKondakjiWunderlich, author = {Gabih, Abdelali and Kondakji, Hakam and Wunderlich, Ralf}, title = {Asymptotic filter behavior for high-frequency expert opinions in a market with Gaussian drift, Stochastic Models}, series = {Stochastic Models}, volume = {36}, journal = {Stochastic Models}, number = {4}, issn = {1532-6349}, doi = {10.1080/15326349.2020.1758567}, pages = {519 -- 547}, language = {en} } @misc{MastroeniWunderlich, author = {Mastroeni, Loretta and Wunderlich, Ralf}, title = {Introduction to Special Issue on Energy Finance}, series = {Decisions in Economics and Finance}, volume = {44}, journal = {Decisions in Economics and Finance}, number = {2}, issn = {1129-6569}, doi = {10.1007/s10203-021-00367-2}, pages = {1015 -- 1020}, language = {en} } @misc{SassWestphalWunderlich, author = {Sass, J{\"o}rn and Westphal, Dorothee and Wunderlich, Ralf}, title = {Diffusion approximations for randomly arriving expert opinions in a financial market with Gaussian drift}, series = {Journal of Applied Probability}, volume = {58}, journal = {Journal of Applied Probability}, number = {1}, issn = {1475-6072}, doi = {10.1017/jpr.2020.82}, pages = {197 -- 216}, language = {en} } @misc{TakamWunderlichMenoukeuPamen, author = {Takam, Paul Honor{\´e} and Wunderlich, Ralf and Menoukeu Pamen, Olivier}, title = {Short-Term Behavior of a Geothermal Energy Storage: Modeling and Theoretical Results}, series = {arXiv.org}, journal = {arXiv.org}, pages = {1 -- 25}, language = {en} } @misc{TakamWunderlichMenoukeuPamen, author = {Takam, Paul Honor{\´e} and Wunderlich, Ralf and Menoukeu Pamen, Olivier}, title = {Short-Term Behavior of a Geothermal Energy Storage: Numerical Applications}, series = {arXiv.org}, journal = {arXiv.org}, pages = {1 -- 28}, language = {en} } @misc{SassWestphalWunderlich, author = {Sass, J{\"o}rn and Westphal, Dorothee and Wunderlich, Ralf}, title = {Diffusion approximations for periodically arriving expert opinions in a financial market with Gaussian drift}, series = {Stochastic Models}, volume = {39}, journal = {Stochastic Models}, issn = {1532-4214}, doi = {10.1080/15326349.2022.2100423}, pages = {323 -- 362}, language = {en} } @misc{TakamWunderlich, author = {Takam, Paul Honor{\´e} and Wunderlich, Ralf}, title = {On the Input-Output Behavior of a Geothermal Energy Storage: Approximations by Model Order Reduction}, series = {arXiv}, journal = {arXiv}, doi = {10.48550/arXiv.2209.14761}, pages = {1 -- 42}, language = {en} } @misc{GabihKondakjiWunderlich, author = {Gabih, Abdelali and Kondakji, Hakam and Wunderlich, Ralf}, title = {Well Posedness of Utility Maximization Problems Under Partial Information in a Market with Gaussian Drift}, series = {arXiv}, journal = {arXiv}, doi = {10.48550/arXiv.2205.08614}, pages = {1 -- 17}, language = {en} } @misc{TakamWunderlichMenoukeuPamen, author = {Takam, Paul Honor{\´e} and Wunderlich, Ralf and Menoukeu Pamen, Olivier}, title = {Modeling and simulation of the input-output behavior of a geothermal energy storage}, series = {Mathematical Methods in the Applied Sciences}, volume = {47}, journal = {Mathematical Methods in the Applied Sciences}, number = {1}, issn = {0170-4214}, doi = {10.1002/mma.9661}, pages = {371 -- 396}, language = {en} } @misc{LamertAuerWunderlich, author = {Lamert, Kerstin and Auer, Benjamin R. and Wunderlich, Ralf}, title = {Discretization of continuous-time arbitrage strategies in financial markets with fractional Brownian motion}, series = {arXiv}, journal = {arXiv}, doi = {10.48550/arXiv.2311.15635}, pages = {1 -- 32}, language = {en} } @misc{GabihKondakjiWunderlich, author = {Gabih, Abdelali and Kondakji, Hakam and Wunderlich, Ralf}, title = {Power Utility Maximization with Expert Opinions at Fixed Arrival Times in a Market with Hidden Gaussian Drift}, series = {arXiv}, journal = {arXiv}, doi = {10.48550/arXiv.2301.06847}, pages = {1 -- 33}, language = {en} } @misc{TakamWunderlich, author = {Takam, Paul Honore and Wunderlich, Ralf}, title = {Model order reduction for the input-output behavior of a geothermal energy storage}, series = {Journal of Engineering Mathematics}, volume = {148}, journal = {Journal of Engineering Mathematics}, number = {1}, publisher = {Springer Science and Business Media LLC}, issn = {0022-0833}, doi = {10.1007/s10665-024-10398-4}, pages = {1 -- 34}, language = {en} } @misc{GabihKondakjiWunderlich, author = {Gabih, Abdelali and Kondakji, Hakam and Wunderlich, Ralf}, title = {Power utility maximization with expert opinions at fixed arrival times in a market with hidden Gaussian drift}, series = {Annals of Operations Research}, volume = {341}, journal = {Annals of Operations Research}, number = {2-3}, publisher = {Springer Science and Business Media LLC}, issn = {0254-5330}, doi = {10.1007/s10479-024-06172-5}, pages = {897 -- 936}, language = {en} } @misc{TakamWunderlich, author = {Takam, Paul Honore and Wunderlich, Ralf}, title = {Numerical simulation of the input-output behavior of a geothermal energy storage}, series = {Energies}, volume = {18}, journal = {Energies}, number = {6}, publisher = {MDPI AG}, issn = {1996-1073}, doi = {10.3390/en18061558}, pages = {1558}, abstract = {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.}, language = {en} } @misc{OuaboKamkumoMbouandiNjiasseWunderlich, author = {Ouabo Kamkumo, Florent and Mbouandi Njiasse, Ibrahim and Wunderlich, Ralf}, title = {Stochastic epidemic models with partial information}, series = {arXiv}, journal = {arXiv}, doi = {10.48550/arXiv.2503.07251}, pages = {1 -- 55}, abstract = {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.}, language = {en} } @misc{MbouandiNjiasseOuaboKamkumoWunderlich, author = {Mbouandi Njiasse, Ibrahim and Ouabo Kamkumo, Florent and Wunderlich, Ralf}, title = {Stochastic optimal control of an epidemic under partial information}, series = {arXiv}, journal = {arXiv}, doi = {10.48550/arXiv.2503.06804}, pages = {1 -- 52}, abstract = {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.}, language = {en} } @misc{TakamWunderlich, author = {Takam, Paul Honor{\´e} and Wunderlich, Ralf}, title = {Cost-optimal management of a residential heating system with a geothermal energy storage under uncertainty}, series = {arXiv}, journal = {arXiv}, doi = {10.48550/arXiv.2502.19619}, pages = {1 -- 41}, language = {en} } @misc{PillingBaehrWunderlich, author = {Pilling, Eric and B{\"a}hr, Martin and Wunderlich, Ralf}, title = {Stochastic optimal control of an industrial Power-to-Heat System with high-temperature heat pump and thermal energy storage}, series = {arXiv}, journal = {arXiv}, doi = {10.48550/arXiv.2411.02211}, pages = {1 -- 63}, abstract = {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.}, language = {en} } @misc{LamertAuerWunderlich, author = {Lamert, Kerstin and Auer, Benjamin R. and Wunderlich, Ralf}, title = {Discretization of continuous-time arbitrage strategies in financial markets with fractional Brownian motion}, series = {Mathematical Methods of Operations Research}, volume = {2025}, journal = {Mathematical Methods of Operations Research}, publisher = {Springer Science and Business Media LLC}, issn = {1432-2994}, doi = {10.1007/s00186-025-00889-0}, pages = {56}, language = {en} } @misc{GabihWunderlich, author = {Gabih, Abdelali and Wunderlich, Ralf}, title = {Portfolio optimization in a market with hidden Gaussian drift and randomly arriving expert opinions}, series = {Annals of operations research}, volume = {2025}, journal = {Annals of operations research}, publisher = {Springer}, address = {Dordrecht}, issn = {1572-9338}, doi = {10.1007/s10479-025-06796-1}, pages = {1 -- 33}, abstract = {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.}, language = {en} } @misc{MbouandiNjiasseOuaboKamkumoWunderlich, author = {Mbouandi Njiasse, Ibrahim and Ouabo Kamkumo, Florent and Wunderlich, Ralf}, title = {Convergence of the extended Kalman filter with small and state-dependent noise}, publisher = {arXiv}, address = {Ithaca, NY}, doi = {10.48550/arXiv.2511.10814}, pages = {1 -- 21}, abstract = {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.}, language = {en} } @misc{AcholaOluochOuaboKamkumoWunderlich, author = {Achola Oluoch, Lillian and Ouabo Kamkumo, Florent and Wunderlich, Ralf}, title = {Stochastic models and estimation of undetected infections in the transmission of Zika virus}, publisher = {arXiv}, address = {Ithaca, NY}, doi = {10.48550/arXiv.2511.01920}, pages = {1 -- 49}, abstract = {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.}, language = {en} } @misc{OuaboKamkumoMbouandiNjiasseWunderlich, author = {Ouabo Kamkumo, Florent and Mbouandi Njiasse, Ibrahim and Wunderlich, Ralf}, title = {Estimating unobservable states in stochastic epidemic models with partial information}, publisher = {arXiv}, address = {Ithaca, NY}, doi = {10.48550/arXiv.2506.00906}, pages = {1 -- 32}, abstract = {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.}, language = {en} }