Related papers: A quantum model for the stock market
It is known that the impact of transactions on stock price (market impact) is a concave function of the size of the order, but there exists little quantitative theory that suggests why this is so. I develop a quantitative theory for the…
Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the…
This paper tends to define the quantitative relationship between the stock price and time as a time function. Based on the empirical evidence that the log-return of a stock is the series of white noise, a mathematical model of the integral…
We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states. Traditional quantum…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
We develop a general framework for applying the Kelly criterion to stock markets. By supplying an arbitrary probability distribution modeling the future price movement of a set of stocks, the Kelly fraction for investing each stock can be…
In this paper I explain how I usually introduce the Schr\"odinger equation during the quantum mechanics course. My preferred method is the chronological one. Since the Schr\"odinger equation belongs to a special case of wave equations I…
Quantum systems with real energies generated by an apparently non-Hermitian Hamiltonian may re-acquire the consistent probabilistic interpretation via an ad hoc metric which specifies the set of observables in the updated Hilbert space of…
We pose the estimation and predictability of stock market performance. Three cases are taken: US, Japan, Germany, the monthly index of the value of realized investment in stocks, prices plus the value of dividend payments (OECD data). Once…
This paper presents a global optimization approach to quantum mechanics, which describes the most fundamental dynamics of the universe. It suggests that the wave-like behavior of (sub)atomic particles could be the critical characteristic of…
We use a $\phi^{4}$ quantum field theory with inhomogeneous couplings and explicit symmetry-breaking to model an ensemble of financial time series from the S$\&$P 500 index. The continuum nature of the $\phi^4$ theory avoids the…
In an equity market model with "Knightian" uncertainty regarding the relative risk and covariance structure of its assets, we characterize in several ways the highest return relative to the market that can be achieved using nonanticipative…
Several problems arising in Economics and Finance are analyzed using concepts and quantitative methods from Physics. Here is the abridged abstact: Chapter 1: By analogy with energy, the equilibrium probability distribution of money must…
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…
An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on…
It is well known that Schr\"{o}dinger's equation is only suitable for the particle in conservative force field. In atomic and molecular field, a particle can suffer the action of non-conservative force. In this paper, a new quantum wave…
Treating macro-black hole as quantum states, and using Brown-York quaselocal gravitational energy definition and Heisenberg uncertainty principle, we find out the classical horizon with singularity spreads into a quantum horizon in which…
The recent crash demonstrated (once again) that the description of the financial market by present financial mathematics cannot be considered as totally satisfactory. We remind that nowadays financial mathematics is heavily based on the use…
The single field chaotic inflation model with a monomial power greater than one seems to be ruled out by the recent Planck and WMAP CMB data while Starobinsky model with a higher curvature term seems to be a viable model. Higher curvature…
We study in detail and explicitly solve the version of Kyle's model introduced in a specific case in \cite{BB}, where the trading horizon is given by an exponentially distributed random time. The first part of the paper is devoted to the…