Related papers: A new decomposition of portfolio return
A {log-optimal} portfolio is any portfolio that maximizes the expected logarithmic growth (ELG) of an investor's wealth. This maximization problem typically assumes that the information of the true distribution of returns is known to the…
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…
Functional decomposition of logic circuits has profound influence on all quality aspects of the cost-effective implementation of modern digital systems. In this paper, a relational approach to the decomposition of logic circuits is…
We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for…
Empirical studies indicate the existence of long range dependence in the volatility of the underlying asset. This feature can be captured by modeling its return and volatility using functions of a stationary fractional Ornstein--Uhlenbeck…
A proportional wealth tax - a levy on the stock of wealth - preserves portfolio neutrality by acting as a uniform drift shift in the Fokker-Planck equation for wealth dynamics. We extend this result to the full system of ownership taxes…
In the present paper we propose a new approach to investigate the logistic function, commonly used in mathematical models in economics and management. The approach is based on indicating in a given time series, having a logistic trend, some…
We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q. Stocks are sold and…
We develop a framework for stochastic portfolio theory (SPT), which incorporates modern nonlinear price impact and impact decay models. Our main result is the derivation of the celebrated master formula for additive functional generation of…
This work derives an approximate analytical single period solution of the portfolio choice problem for the power utility function. It is possible to do so if we consider that the asset returns follow a multivariate normal distribution. It…
This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depend on an external process of economic factors. There are transaction costs with a structure that…
In this paper, we are interested in continuous time models in which the index level induces some feedback on the dynamics of its composing stocks. More precisely, we propose a model in which the log-returns of each stock may be decomposed…
The powers of generating functions and its properties are analyzed. A new class of functions is introduced, based on the application of compositions of an integer $n$, called composita. The methods for obtaining reciprocal and reverse…
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
We introduce polynomial processes in the sense of [8] in the context of stochastic portfolio theory to model simultaneously companies' market capitalizations and the corresponding market weights. These models substantially extend volatility…
We revisit the classical Merton consumption--investment problem when risky-asset returns are modeled by stochastic differential equations interpreted through a general $\alpha$-integral, interpolating between It\^{o}, Stratonovich, and…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
We review various methods to investigate the statics and the dynamics of collective composition fluctuations in dense polymer mixtures within fluctuating-field approaches. The central idea of fluctuating-field theories is to rewrite the…
We show that if a random variable is the final value of an adapted log-H\"{o}lder continuous process, then it can be represented as a stochastic integral with respect to a fractional Brownian motion with adapted integrand. In order to…
A new type of an integrable mapping is presented. This map is equipped with fractional difference and possesses an exact solution, which can be regarded as a discrete analogue of the Mittag-Leffler function.