Related papers: A new decomposition of portfolio return
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady-state by using joint probability distributions symmetries of different entropy production decompositions. The analytical approach is…
We study stochastic monotonicity and propagation of order for Markov processes with respect to stochastic integral orders characterized by cones of functions satisfying $\Phi f \geq 0$ for some linear operator $\Phi$. We introduce a new…
In our previous studies we have investigated the structural complexity of time series describing stock returns on New York's and Warsaw's stock exchanges, by employing two estimators of Shannon's entropy rate based on Lempel-Ziv and Context…
In the context of stochastic portfolio theory we introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios which are determined by certain transformations of linear functions of a…
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal…
The generating functional is derived for the fluctuation-dissipation relations which result from the unitarity and reversibility of microscopic dynamics and connect various statistical characteristics of many consecutive (continuous)…
We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part,…
A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities,…
Modern generative models can be understood as probability transport from a simple base distribution to a target data distribution. Deterministic transport models offer tractable velocity-field parameterizations, whereas stochastic…
We consider a family of fragmentation processes where the rate at which a particle splits is proportional to a function of its mass. Let $F\_{1}^{(m)}(t),F\_{2}^{(m)}(t),...$ denote the decreasing rearrangement of the masses present at time…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
We give a short overview of recent developments in exact solutions for macroscopic fluctuation theory by using connections to classical integrable systems. A calculation of the cumulant generating function for a tagged particle is also…
Managing investment portfolios is an old and well know problem in multiple fields including financial mathematics and financial engineering as well as econometrics and econophysics. Multiple different concepts and theories were used so far…
Recent developments in deep learning techniques have motivated intensive research in machine learning-aided stock trading strategies. However, since the financial market has a highly non-stationary nature hindering the application of…
The statistical properties of a stochastic process may be described (1)by the expectation values of the observables, (2)by the probability distribution functions or (3)by probability measures on path space. Here an analysis of level (3) is…
Diffusion models have recently achieved remarkable success in generative modeling, yet they are commonly formulated as black-box stochastic systems with limited interpretability and few structural guarantees. In this paper, we establish a…
A fractal approach to the long-short portfolio optimization is proposed. The algorithmic system based on the composition of market-neutral spreads into a single entity was considered. The core of the optimization scheme is a fractal walk…
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…