arXiv subjects

Svetlana Malysheva

Publications and source records attributed to Svetlana Malysheva.

3 recordsLinked to original sources

arXiv2024

Eigenvalue statistics of Elliptic Volatility Model with power-law tailed volatility

In this paper we study an ensemble of random matrices called Elliptic Volatility Model, which arises in finance as models of stock returns. This model consists of a product of independent matrices $X = ΣZ $ where $Z$ is a $T$ by $S$ matrix of i.i.d. light-tailed variables with mean 0 and variance 1 and $Σ$ is a diagonal matrix. In this paper, we take the randomness of $Σ$ to be i.i.d. heavy tailed. We obtain an explicit formula for the empirical spectral distribution of $X^*X$ in the particular case when the elements of $Σ$ are distributed as Student's t with parameter 3. We furthermore obtain the distribution of the largest eigenvalue in more general case, and we compare our results to financial data.

math.PR↗

arXiv2023

Central Limit Theorem for traces of the resolvents of half-heavy tailed Sample Covariance matrices

We consider the spectrum of the Sample Covariance matrix $\mathbf{A}_N:= \frac{\mathbf{X}_N \mathbf{X}_N^*}{N}, $ where $\mathbf{X}_N$ is the $P\times N$ matrix with i.i.d. half-heavy tailed entries and $\frac{P}{N}\to y>0$ (the entries of the matrix have variance, but do not have the fourth moment). We derive the Central Limit Theorem for the Stieltjes transform of the matrix $\mathbf{A}_N$ and compute the covariance kernel. Apart from that, we derive the Central Limit Theorem for the Stieltjes transform of overlapping Sample Covariance matrices.

math.PR↗

arXiv2023

A metric for tradable biodiversity credits linked to the Living Planet Index and global species conservation

Difficulties identifying appropriate biodiversity impact metrics remain a major barrier to inclusion of biodiversity considerations in environmentally responsible investment. We propose and analyse a simple science-based local metric: the sum of proportional changes in local species abundances relative to their global species abundances, with a correction for species close to extinction. As we show, this metric quantifies changes in the mean long-term global survival probability of species. It links mathematically to a widely cited global biodiversity indicator, the Living Planet Index, for which we propose an improved formula that directly addresses the known problem of singularities caused by extinctions. We show that, in an ideal market, trade in our metric would lead to near-optimal allocation of resources to species conservation. We further show that the metric is closely related to several other metrics and indices already in use. Barriers to adoption are therefore low. Used in conjunction with metrics addressing ecosystem functioning and services, potential areas of application include biodiversity related financial disclosures and voluntary or legislated no net biodiversity loss policies.

q-bio.PE↗