Related papers: A new decomposition of portfolio return
We propose a novel method to improve estimation of asset returns for portfolio optimization. This approach first performs a monthly directional market forecast using an online decision tree. The decision tree is trained on a novel set of…
The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…
Financial institutions and insurance companies that analyze the evolution and sources of profits and losses often look at risk factors only at discrete reporting dates, ignoring the detailed paths. Continuous-time decompositions avoid this…
We study long-term growth-optimal strategies on a simple market with linear proportional transaction costs. We show that several problems of this sort can be solved in closed form, and explicit the non-analytic dependance of optimal…
Extending the idea of Even and Lehrer [3], we discuss a general approach to integration based on a given decomposition system equipped with a weighting function, and a decomposition of the integrated function. We distinguish two type of…
Convolution admits a natural formulation as a functional operation on matrices. Motivated by the functional and entrywise calculi, this leads to a framework in which convolution defines a matrix transform that preserves positivity. Within…
If a complex analytic function, $f$, has a stratified isolated critical point, then it is known that the cohomology of the Milnor fibre of $f$ has a direct sum decomposition in terms of the normal Morse data to the strata. We use microlocal…
We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk…
Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a…
The correlation matrix formalism is used to study temporal aspects of the stock market evolution. This formalism allows to decompose the financial dynamics into noise as well as into some coherent repeatable intraday structures. The present…
We forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions for processes as contraction operators on a complete metric…
Buying or selling assets leads to transaction costs for the investor. On one hand, it is well know to all market practionaires that the transaction costs are positive on average and present therefore systematic loss. On the other hand, for…
Expectations of marginals conditional on the total risk of a portfolio are crucial in risk-sharing and allocation. However, computing these conditional expectations may be challenging, especially in critical cases where the marginal risks…
Generalized numbers, arithmetic operators and derivative operators, grouped in four classes based on symmetry features, are introduced. Their building element is the pair of $q$-logarithm/$q$-exponential inverse functions. Some of the…
Financial markets are interconnected, with micro-currents propagating across global markets and shaping economic trends. This paper moves beyond traditional stock market indices to examine cross-sectional return distributions-15 in our…
This paper derives an optimal portfolio that is based on trend-following signal. Building on an earlier related article, it provides a unifying theoretical setting to introduce an autocorrelation model with the covariance matrix of trends…
This paper aims to develop new mathematical and computational tools for modeling the distribution of portfolio returns across portfolios. We establish relevant mathematical formulas and propose efficient algorithms, drawing upon powerful…
It has been widely observed that capitalization-weighted indexes can be beaten by surprisingly simple, systematic investment strategies. Indeed, in the U.S. stock market, equal-weighted portfolios, random-weighted portfolios, and other…
We introduce a new class of forward performance processes that are endogenous and predictable with regards to an underlying market information set and, furthermore, are updated at discrete times. We analyze in detail a binomial model whose…
Productions functions map the inputs of a firm or a productive system onto its outputs. This article expounds generalizations of the production function that include state variables, organizational structures and increasing returns to…