Related papers: A Quantum Approach to Stock Price Fluctuations
Fluctuation theorems show how coarse graining transforms microscopic symmetry into observable irreversibility. Here we ask whether an analogous symmetrybased diagnostic can be constructed for financial markets. At the microscopic level,…
Factorial moments are convenient tools in nuclear physics to characterize the multiplicity distributions when phase-space resolution ($\Delta$) becomes small. For uncorrelated particle production within $\Delta$, Gaussian statistics holds…
We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting,…
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two…
A statistical physics model for the time evolutions of stock portfolios is proposed. In this model the time series of price changes are coded into the sequences of up and down spins. The Hamiltonian of the system is introduced and is…
The Sharpe ratio, which is defined as the ratio of the excess expected return of an investment to its standard deviation, has been widely cited in the financial literature by researchers and practitioners. However, very little attention has…
Quantum backflow is a counterintuitive phenomenon in which the probability density of a quantum particle propagates opposite to its momentum. Experimental observation of backflow has remained elusive due to two main challenges: (i) the…
Quantum dynamics of the collective mode and individual particles on a ring is studied as the simplest model of projective quantum measurement. In this model, the collective mode measures an individual single quantum system. The heart of the…
A theory which describes the share price evolution at financial markets as a continuous-time random walk has been generalized in order to take into account the dependence of waiting times t on price returns x. A joint probability density…
Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as atmospheric flows, heartbeat patterns, population dynamics, etc. The physics of the long-range correlations intrinsic to fractal fluctuations is…
We uncover the quantum fluctuation-response inequality, which, in the most general setting, establishes a bound for the mean difference of an observable at two different quantum states, in terms of the quantum relative entropy. When the…
Let $N(L)$ be the number of eigenvalues, in an interval of length $L$, of a matrix chosen at random from the Gaussian Orthogonal, Unitary or Symplectic ensembles of ${\cal N}$ by ${\cal N}$ matrices, in the limit ${\cal…
A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such…
In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining…
We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this…
Dow Jones Index time series exhibit irregular or fractal fluctuations on all time scales from days, months to years. The nonlinear fluctuations are selfsimilar as exhibited in inverse power law form for power spectra of temporal…
We present a quantum field theoretical derivation of the nondecay probability of an unstable particle with nonzero three-momentum $\mathbf{p}$. To this end, we use the (fully resummed) propagator of the unstable particle, denoted as $S,$ to…
The value of stocks, indices and other assets, are examples of stochastic processes with unpredictable dynamics. In this paper, we discuss asymmetries in short term price movements that can not be associated with a long term positive trend.…
We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with…
The equation of state with quantum statistics corrections is used for particle number fluctuations $\omega$ of isotopically symmetric nuclear matter with interparticle van der Waals and Skyrme local density interactions. The fluctuations,…