相关论文: Stock Mechanics: a classical approach

The importance of predicting stock market prices cannot be overstated. It is a pivotal task for investors and financial institutions as it enables them to make informed investment decisions, manage risks, and ensure the stability of the…

Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility…

It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes…

We present a new model for prediction markets, in which we use risk measures to model agents and introduce a market maker to describe the trading process. This specific choice on modelling tools brings us mathematical convenience. The…

In this paper we seek to demonstrate the predictability of stock market returns and explain the nature of this return predictability. To this end, we introduce investors with different investment horizons into the news-driven, analytic,…

Some elements of classical mechanics and classical statistical mechanics are formulated in terms of fibre bundles. In the bundle approach the dynamical and distribution functions are replaced by liftings of paths in a suitably chosen…

Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns.…

Financial networks have become extremely useful in characterizing the structure of complex financial systems. Meanwhile, the time evolution property of the stock markets can be described by temporal networks. We utilize the temporal network…

The use of kinetic modelling based on partial differential equations for the dynamics of stock price formation in financial markets is briefly reviewed. The importance of behavioral aspects in market booms and crashes and the role of…

The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic…

Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of L\'{e}vy driven models of stock markets. In our opinion, any market model should be based on a…

We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather…

One of the pillars to build a country's economy is the stock market. Over the years, people are investing in stock markets to earn as much profit as possible from the amount of money that they possess. Hence, it is vital to have a…

A stock market is considered as one of the highly complex systems, which consists of many components whose prices move up and down without having a clear pattern. The complex nature of a stock market challenges us on making a reliable…

Macroscopic properties of equity markets affect the performance of active equity strategies but many are not adequately captured by conventional models of financial mathematics and econometrics. Using the CRSP Database of the US equity…

Financial markets have developed a lot of strategies to control risks induced by market fluctuations. Mathematics has emerged as the leading discipline to address fundamental questions in finance as asset pricing model and hedging…

The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…

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…

I find a topological arrangement of stocks traded in a financial market which has associated a meaningful economic taxonomy. The topological space is a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting…

Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large…