Related papers: Utility maximization in Wiener-transformable marke…
We consider an investor who is dynamically informed about the future evolution of one of the independent Brownian motions driving a stock's price fluctuations. With linear temporary price impact the resulting optimal investment problem with…
Optimization of problems with high computational power demands is a challenging task. A probabilistic approach to such optimization called Bayesian optimization lowers performance demands by solving mathematically simpler model of the…
Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness…
We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as…
We study a continuous-time expected utility maximization problem in which the investor at maturity receives the value of a contingent claim in addition to the investment payoff from the financial market. The investor knows nothing about the…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
We present a Markovian market model driven by a hidden Brownian efficient price. In particular, we extend the queue-reactive model, making its dynamics dependent on the efficient price. Our study focuses on two sub-models: a signal-driven…
Using the white noise space framework, we define a class of stochastic processes which include as a particular case the fractional Brownian motion and its derivative. The covariance functions of these processes are of a special form,…
Obtaining utility maximizing optimal portfolios in closed form is a challenging issue when the return vector follows a more general distribution than the normal one. In this note, we give closed form expressions, in markets based on…
We propose a practical Bayesian optimization method using Gaussian process regression, of which the marginal likelihood is maximized where the number of model selection steps is guided by a pre-defined threshold. Since Bayesian optimization…
This paper considers the problem of reconstructing missing parts of functions based on their observed segments. It provides, for Gaussian processes and arbitrary bijective transformations thereof, theoretical expressions for the…
Financial markets have long since been modeled using stochastic methods such as Brownian motion, and more recently, rough volatility models have been built using fractional Brownian motion. This fractional aspect brings memory into the…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
In an incomplete financial market with general continuous semimartingale dynamics; we model an investor with log-utility preferences who, in addition to an initial capital, receives units of a non-traded endowment process. Using duality…
Energy market designs with non-merchant storage have been proposed in recent years, with the aim of achieving optimal market integration of storage. In order to handle the time-linking constraints that are introduced in such markets,…
Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and…
The non-storability of electricity makes it unique among commodity assets, and it is an important driver of its price behaviour in secondary financial markets. The instantaneous and continuous matching of power supply with demand is a key…
Gaussian process classification is a popular method with a number of appealing properties. We show how to scale the model within a variational inducing point framework, outperforming the state of the art on benchmark datasets. Importantly,…
Brownian motion is the only random process which is Gaussian, stationary and Markovian. Dropping the Markovian property, i.e. allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst…
We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval…