The Corvinus Centre for Operations Research (CCOR), the Corvinus Institute for Advanced Studies (CIAS) and the Institute of Operations and Decision Sciences invites you to the
CCOR Workshop titled Models, Applications and Computing.
Venue: Corvinus University of Budapest, Building C, Room: C.714
Date: January 8, 2025 (Wednesday), 13:00 – 15:30
Keynote speaker: Csaba Farkas (Sapientia Hungarian University of Transylvania)
Speakers: Miklós Pintér (Corvinus University of Budapest) and Roland Török (Corvinus University of Budapest)
Programme:
13:00 – 14:00: Csaba Farkas: Hardy Inequality and Its Variants
14:00 – 14:30: Coffee break
14:30 – 15:00: Miklós Pintér: A portfolio optimization application
15:00 – 15:30: Roland Török: Implementation of predictor-corrector interior-point algorithms for solving P*(K)-linear complementarity problems
Abstracts
Csaba Farkas: Hardy Inequality and Its Variants
The Hardy inequality is a fundamental result in mathematical analysis, concerning the integration of functions and the associated weight functions. It is named after the English mathematician G. H. Hardy. In this talk, we will present the proof of the original form of the Hardy inequality and explore its modern variants and applications, including the Hardy-Rellich inequality. Subsequently, we will extend the analysis to curved spaces, with a focus on its validity and applications in Riemannian and Finsler manifolds. The presentation will conclude with an exploration of the interpolation between the Hardy inequality and the Moser-Trudinger inequality.
Miklós Pintér: A portfolio optimization application
The talk aims to outline a financial application of critical point theory. Our starting point is the classical Markowitz portfolio optimization problem (Markowitz, 1952). We then address a problem where the ”expected value” of a portfolio is significantly influenced by the so-called price effect. In other words, the ”value” of a portfolio is measured by its cash-equivalent portfolio, taking into account the cost of liquidation. Liquidity recommendations are incorporated (Acerbi and Scandolo, 2008; Csóka and Herings, 2014), meaning that these recommendations define a feasible set of portfolios. Importantly, we allow the feasibility set to be non-convex.
The objective is to minimize risk under the given liquidity recommendations. The risk of a portfolio is evaluated using coherent risk measures. Over any reasonable feasibility set defined by liquidity recommendations, a coherent risk measure forms a seminorm. Thus, we summarize the proposed application as a constrained optimization problem, where the objective function is a seminorm, and the feasibility set is a subset of a Banach space (with portfolios represented as continuous functions).
References
Acerbi C, Scandolo G (2008) Liquidity risk theory and coherent measures of risk. Quantitative Finance 8:681–692
Csóka P, Herings JJ (2014) Risk allocation under liqudity considerations. Journal of Banking and Finance 49:1–9
Markowitz H (1952) Portfolio selection. The Journal of Finance 7(1):77–91
Roland Török: Implementation of predictor-corrector interior-point algorithms for solving P*(K)-linear complementarity problems
In the first part of the presentation we show our theoretical results about a predictor-corrector interior-point algorithm (PC IPA) for solving P*(K)-linear complementarity problems (LCPs) based on a new class of algebraically equivalent transformation (AET) functions. In the second part of the presentation we present our numerical results on a newly generated test set of problems. We compare the PC IPA based on three different AET functions from the new class of AETs with a PC IPA that is based on a kernel function from the literature. In all cases, we obtain promising numerical results.