Related papers: Portfolio Theory, Information Theory and Tsallis S…
With the fast development of quantitative portfolio optimization in financial engineering, lots of AI-based algorithmic trading strategies have demonstrated promising results, among which reinforcement learning begins to manifest…
Motivated by the current fears of a potentially stagflationary global economic environment, this paper uses new and recently introduced mathematical techniques to study multivariate time series pertaining to country inflation (CPI),…
With the advent of Web 2.0, various types of data are being produced every day. This has led to the revolution of big data. Huge amount of structured and unstructured data are produced in financial markets. Processing these data could help…
A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a…
We hypothesize that portfolio sorts based on the V/P ratio generate excess returns and consist of companies that are undervalued for prolonged periods. Results, for the US market show that high V/P portfolios outperform low V/P portfolios…
Although maximizing median and quantiles is intuitively appealing and has an axiomatic foundation, it is difficult to study the optimal portfolio strategy due to the discontinuity and time inconsistency in the objective function. We use the…
We study the excess growth rate -- a fundamental logarithmic functional arising in portfolio theory -- from the perspective of information theory. We show that the excess growth rate can be connected to the R\'{e}nyi and cross entropies,…
Portfolio selection problems that optimize expected utility are usually difficult to solve. If the number of assets in the portfolio is large, such expected utility maximization problems become even harder to solve numerically. Therefore,…
By using Random Matrix Theory, we build covariance matrices between stocks of the BM&F-Bovespa (Bolsa de Valores, Mercadorias e Futuros de S\~ao Paulo) which are cleaned of some of the noise due to the complex interactions between the many…
The question addressed in this paper is the performance of the optimal strategy, and the impact of partial information. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable…
Nonadditive Tsallis $q$-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticised by some authors based on the…
The stock market offers a platform where people buy and sell shares of publicly listed companies. Generally, stock prices are quite volatile; hence predicting them is a daunting task. There is still much research going to develop more…
An algorithm was recently introduced by INTECH for the purposes of estimating the trading-profit contribution of systematic rebalancing to the relative return of rules-based investment strategies. We apply this methodology to analyze the…
We study the average asymptotic growth rate of cells in randomly fluctuating environments, with multiple viable phenotypes per environment. We show that any information processing strategy has an asymptotic growth rate, which is the sum of:…
The most commonly accepted model for investors' preferences is expected utility theory. More recently, other theories have emerged and pose new challenges to mathematics. The present paper treats preferences of cumulative prospect theory…
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate…
I discuss some theoretical results with a view to motivate some practical choices in portfolio optimization. Even though the setting is not completely general (for example, the covariance matrix is assumed to be non-singular), I attempt to…
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic volatility and unknown stock appreciation rate. The volatility parameter is driven by an external economic factor modeled as a…
We analyze the theory of optimal investment in risky assets, developed recently by Marsili, Maslov and Zhang [Physica A 253 (1998) 403]. When the real data are used instead of abstract stochastic process, it appears that a non-trivial…
From the Hamilton-Jacobi-Bellman equation for the value function we derive a non-linear partial differential equation for the optimal portfolio strategy (the dynamic control). The equation is general in the sense that it does not depend on…