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Ignas Gasparavičius

Publications and source records attributed to Ignas Gasparavičius.

3 recordsLinked to original sources
arXiv2026

Generalizing Markowitz Portfolio Optimization by a Quadratic Risk Measure

We show that the key optimization results of the classical Markowitz portfolio selection theory, originally formulated for variance as the risk measure, remain available in explicit closed form under a broader class of strictly convex quadratic risk measures. The proposed framework replaces the covariance matrix with an arbitrary symmetric positive definite matrix and allows additional linear and constant terms, thereby containing various models arising in transaction cost optimization, benchmark relative optimization, covariance regularization, and factor models. Closed-form formulas are obtained for the efficient frontier, the global minimum risk portfolio, the maximum Sharpe ratio portfolio, the Capital Market Curve, the tangency portfolio, and the maximum utility portfolio. In contrast to the classical Markowitz model, the tangency portfolio does not coincide with the maximum Sharpe ratio portfolio, revealing a new geometric phenomenon. A numerical example confirms the derived formulas.

q-fin.PM↗
arXiv2025

Picturesque convolution-like recurrences and partial sums' generation

Let ${\pmb b}=\{b_0,\,b_1,\,\ldots\}$ be the known sequence of numbers such that $b_0\neq0$. In this work, we develop methods to find another sequence ${\pmb a}=\{a_0,\,a_1,\,\ldots\}$ that is related to ${\pmb b}$ as follows: $a_n=a_0\,b_{n+m}+a_1\,b_{n+m-1}+\ldots+a_{n+m}\,b_0$, $n\in\mathbb{N}\cup\{0\}$, $m\in\mathbb{N}$. We show the connection of $\lim_{n\to\infty}a_n$ with $a_0,\,a_1,\,\ldots,\,a_{m-1}$ and provide varied examples of finding the sequence ${\pmb a}$ when ${\pmb b}$ is given. We demonstrate that the sequences ${\pmb a}$ may exhibit pretty patterns in the plane or space. Also, we show that the properly chosen sequence ${\pmb b}$ may define ${\pmb a}$ as some famous sequences, such as the partial sums of the Riemann zeta function, etc.

math.NT↗