相关论文: A mathematical study of the excess growth rate
Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth…
In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that…
This paper characterizes the best possible rate of growth of wealth in a Kelly betting game when repeatedly betting against a general i.i.d. null hypothesis $\mathscr{P}$, but the data are drawn i.i.d from an arbitrary alternative $Q$. We…
It is well-known that there are a number of relations between theoretical finance theory and information theory. Some of these relations are exact and some are approximate. In this paper we will explore some of these relations and determine…
We strengthen the maximal ergodic theorem for actions of groups of polynomial growth to a form involving jump quantity, which is the sharpest result among the family of variational or maximal ergodic theorems. As a consequence, we deduce in…
We review some fundamental concepts of investment from a mathematical perspective, concentrating specifically on fractional-Kelly portfolios, which allocate a fraction of wealth to a growth-optimal portfolio while the remainder collects (or…
A relationship between the growth-rate of logoptimal portfolios and capacity of fading single-input multiple output (SIMO) channels are established. Using this relation, stock vector stochastic processes that model the investment…
In finance, one usually deals not with prices but with growth rates $R$, defined as the difference in logarithm between two consecutive prices. Here we consider not the trading volume, but rather the volume growth rate $\tilde R$, the…
We study population dynamics through a general growth/degrowth-fragmentation process, with resource consumption and unbounded growth/degrowth, birth and death rates. Our model is structured in a positive trait called energy (which is a…
In the context of a large class of stochastic processes used to describe the dynamics of wealth growth, we prove a set of inequalities establishing necessary and sufficient conditions in order to avoid infinite wealth concentration. These…
We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, It\^{o}-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk}…
A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a super-position of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency…
The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and…
Turnpike theorems state that if an investor's utility is asymptotically equivalent to a power utility, then the optimal investment strategy converges to the CRRA strategy as the investment horizon tends to infinity. This paper aims to…
The theory of transient growth describes how linear mechanisms can cause temporary amplification of disturbances even when the linearized system is asymptotically stable as defined by its eigenvalues. This growth is traditionally quantified…
Within its range of applicability, the Boltzmann equation seems unique in its capacity to accurately describe the transition from almost any initial state to a self-equilibrated thermal state. Using information-theoretic methods to rephrase…
Ergodicity economics is a new branch of economic theory that notes the conceptual difference between time averages and expectation values, which coincide only for ergodic observables. It postulates that individual agents maximise the time…
We study the continuity property of the generalized entropy as a function of the underlying probability distribution, defined with an action space and a loss function, and use this property to answer the basic questions in statistical…
We analyze the fine-grained connections between the average degree and the power-law degree distribution exponent in growing information networks. Our starting observation is a power-law degree distribution with a decreasing exponent and…
We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to…