Related papers: Stock markets and quantum dynamics: a second quant…
Traders in a market typically have widely different, private information on the return of an asset. The equilibrium price of the asset may reflect this information more accurately if the number of traders is large enough compared to the…
We present a mathematical model of a market with $m$ shares traded across $n$ investor groups, each one with similar motivations and trading strategies. The market of each asset consists of a fixed amount of cash and shares (no additions…
The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
We give three derivations of Polya's approximation for the expected range of a simple random walk in one dimension. This result allows for an estimation of the volatility of a financial instrument from the difference between the high and…
The precise characterization of dynamics in open quantum systems often presents significant challenges, leading to the introduction of various approximations to simplify a model. One commonly used strategy involves Markovian approximations,…
We consider a financial market where the asset price follows a fractional Brownian motion. We introduce a family of investment strategies, and quantify profit possibilities for both persistent and antipersistant markets.
We propose a unified approach to several problems in Stochastic Portfolio Theory (SPT), which is a framework for equity markets with a large number $d$ of stocks. Our approach combines open markets, where trading is confined to the top $N$…
We describe a financial market model which shows a non-equilibrium phase transition. Near the transition punctuated equilibrium behaviour is seen, with avalanches occuring on all scales. This scaling is described by an exponent very near 1.…
Most finance studies are discussed on the basis of several hypotheses, for example, investors rationally optimize their investment strategies. However, the hypotheses themselves are sometimes criticized. Market impacts, where trades of…
In this paper we develop models of asset return mean and covariance that depend on some observable market conditions, and use these to construct a trading policy that depends on these conditions, and the current portfolio holdings. After…
This paper describes the dependence of market-based statistical moments of returns on statistical moments and correlations of the current and past trade values. We use Markowitz's definition of value weighted return of a portfolio as the…
This is a work in progress. The aim is to propose a plausible mechanism for the short term dynamics of the oil market based on the interaction of economic agents. This is a theoretical research which by no means aim at describing all the…
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…
Writing the article-Time independent pricing of options in range bound markets; the question in the title came naturally to my mind. It is stated, in the above article, that in certain market conditions the stock price is subjected to an…
We propose a model for equity trading in a population of agents where each agent acts to achieve his or her target stock-to-bond ratio, and, as a feedback mechanism, follows a market adaptive strategy. In this model only a fraction of…
Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both…
We study a stochastic control approach to managed futures portfolios. Building on the Schwartz 97 stochastic convenience yield model for commodity prices, we formulate a utility maximization problem for dynamically trading a single-maturity…
In this paper, our objective is to develop a multi-agent financial system that incorporates simulated trading, a technique extensively utilized by financial professionals. While current LLM-based agent models demonstrate competitive…
Bohmian mechnaics is the most naively obvious embedding imaginable of Schr\"odingers's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…