Related papers: Bounds on Portfolio Quality
This paper focuses on random projection operators when the subspace of projection is estimated. We derive non-asymptotic upper bounds on the error between the projection onto the estimated subspace and the projection onto the underlying…
Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…
The pure tone hearing threshold is usually estimated from responses to stimuli at a set of standard frequencies. This paper describes a probabilistic approach to the estimation problem in which the hearing threshold is modelled as a smooth…
In this paper we derive tight bounds on the expected value of products of {\em low influence} functions defined on correlated probability spaces. The proofs are based on extending Fourier theory to an arbitrary number of correlated…
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…
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…
In this paper, the mean-variance portfolio selection problem with Poisson jumps are studied, where the recursive utility is given by the solution to a backward stochastic differential equation with Poisson jumps. Both the maximum principle…
This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable,…
We introduce a microscopic model of interacting financial agents, where each agent is characterized by two portfolios; money invested in bonds and money invested in stocks. Furthermore, each agent is faced with an optimization problem in…
We give two upper bounds to the mutual information in arbitrary quantum estimation strategies. The first is based on some simple Fourier properties of the estimation apparatus. The second is derived using the first but, interestingly,…
For normal canonical models with $X \sim N_p(\theta, \sigma^{2} I_{p}), \;\; S^{2} \sim \sigma^{2}\chi^{2}_{k}, \;{independent}$, we consider the problem of estimating $\theta$ under scale invariant squared error loss $\frac{\|d-\theta…
The variance measures the portfolio risks the investors are taking. The investor, who holds his portfolio and doesn't trade his shares, at the current time can use the time series of the market trades that were made during the averaging…
An upper bound on the capacity of multiple-input multiple-output (MIMO) Gaussian fading channels is derived under peak amplitude constraints. The upper bound is obtained borrowing concepts from convex geometry and it extends to MIMO…
Recent advances in quantum hardware offer new approaches to solve various optimization problems that can be computationally expensive when classical algorithms are employed. We propose a hybrid quantum-classical algorithm to solve a dynamic…
The asymptotic distribution of the Markowitz portfolio is derived, for the general case (assuming fourth moments of returns exist), and for the case of multivariate normal returns. The derivation allows for inference which is robust to…
A new outer bound on the capacity region of Gaussian interference channels is developed. The bound combines and improves existing genie-aided methods and is shown to give the sum-rate capacity for noisy interference as defined in this…
We consider the problem of estimating the direction of arrival of a signal embedded in $K$-distributed noise, when secondary data which contains noise only are assumed to be available. Based upon a recent formula of the Fisher information…
Financial stock returns correlations have been studied in the prism of random matrix theory, to distinguish the signal from the "noise". Eigenvalues of the matrix that are above the rescaled Marchenko Pastur distribution can be interpreted…
In this work, we propose a new criterion for choosing the regularization parameter in Tikhonov regularization when the noise is white Gaussian. The criterion minimizes a lower bound of the predictive risk, when both data norm and noise…
As an example of the recently-introduced concept of rate of innovation, signals that are linear combinations of a finite number of Diracs per unit time can be acquired by linear filtering followed by uniform sampling. However, in reality,…