Financial Mathematics III

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: 30 April 2025 | Viewed by 2642

Special Issue Editor


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Guest Editor
Department of Economics, Ca’ Foscari University of Venice, Cannaregio 873, 30121 Venice, Italy
Interests: financial mathematics; option pricing; DEA (data envelopment analysis) models; performance evaluation of mutual funds; credit risk
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Special Issue Information

Dear Colleagues,

In recent years, financial mathematics has become an important field for mathematicians. On the one hand, the development of mathematical and probabilistic models for finance has allowed us to make progress in the classical fields of financial mathematics. Among these, we may refer to the criteria of choice for the best alternatives among investment or financing projects, as well as models for studying, for example, the dynamics of interest rates, the evaluation of bonds, portfolio theory and dynamic asset allocation, the dynamics of stock prices, and the pricing and risk assessment of many derivatives (options, futures, swaps, and a variety of other derivatives).

On the other hand, other important issues require the formulation of mathematical models for studying novel issues that have become relevant, oftentimes hot topics in financial markets. Especially the evaluation and management of the risks to which financial markets are exposed have become crucial factors. Thus, we have discovered innovative models for the evaluation of credit risks for bonds and of bank loans, and models for the assessment of sovereign risks.

In addition, new models to assess the performance of mutual funds make use of different approaches drawn from different fields—among these data envelopment analysis—and enable the study of socially responsible investments. Moreover, the application of several machine learning algorithms to different financial mathematics problems has enabled improvements in financial valuations and pricing.

The purpose of the current Special Issue is to establish a collection of articles that reflect the latest mathematical methods and models in the field of financial mathematics, creating a bridge between mathematical theory and its application to finance.

This Special Issue is a continuation of the previous, successful Special Issue “Financial Mathematics”.

Prof. Dr. Antonella Basso
Guest Editor

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Keywords

  • financial mathematics
  • bonds and interest rates dynamics
  • asset allocation and portfolio theory
  • derivatives and option pricing
  • credit and sovereign risks
  • socially responsible investments
  • performance evaluation of mutual funds
  • data envelopment analysis
  • machine learning algorithms
  • neural networks

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Published Papers (2 papers)

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Research

26 pages, 11376 KiB  
Article
The Effects of the Introduction of Volume-Based Liquidity Constraints in Portfolio Optimization with Alternative Investments
by Diana Barro, Antonella Basso, Stefania Funari and Guglielmo Alessandro Visentin
Mathematics 2024, 12(15), 2424; https://doi.org/10.3390/math12152424 - 4 Aug 2024
Viewed by 781
Abstract
Recently, liquidity issues in financial markets and portfolio asset management have attracted much attention among investors and scholars, fuelling a stream of research devoted to exploring the role of liquidity in investment decisions. In this paper, we aim to investigate the effects of [...] Read more.
Recently, liquidity issues in financial markets and portfolio asset management have attracted much attention among investors and scholars, fuelling a stream of research devoted to exploring the role of liquidity in investment decisions. In this paper, we aim to investigate the effects of introducing liquidity in portfolio optimization problems. For this purpose, first we consider three volume-based liquidity measures proposed in the literature and we build a new one particularly suited to portfolio optimization. Secondly, we formulate an extended version of the Markowitz portfolio selection problem, named mean–variance–liquidity, wherein the goal is to minimize the portfolio variance subject to the usual constraint on the expected portfolio return and an additional constraint on the portfolio liquidity. Thirdly, we consider a sensitivity analysis, with the aim to assess the trade-offs between liquidity and return, on the one hand, and between liquidity and risk, on the other hand. In the second part of the paper, the portfolio optimization framework is applied to a dataset of US ETFs comprising both standard and alternative, often illiquid, investments. The analysis is carried out with all the liquidity measures considered, allowing us to shed light on the relationships among risk, return and liquidity. Finally, we study the effects of the introduction of a Bitcoin ETF, as an asset with an extremely high expected return and risk. Full article
(This article belongs to the Special Issue Financial Mathematics III)
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11 pages, 273 KiB  
Article
Pricing of Al-Urbun and a Class of Al-Istijrar Islamic Contracts under the Black–Scholes Framework
by Joanna Goard and Mohammed AbaOud
Mathematics 2024, 12(2), 252; https://doi.org/10.3390/math12020252 - 12 Jan 2024
Viewed by 1025
Abstract
Islamic financial contracts necessarily need to abide by Shariah principles. As such, some contracts have been introduced for risk-hedging real transactions that differ from those seen in conventional financial markets. In this paper, we examine two such products, Al-Urbun and Al-Istijrar, and determine [...] Read more.
Islamic financial contracts necessarily need to abide by Shariah principles. As such, some contracts have been introduced for risk-hedging real transactions that differ from those seen in conventional financial markets. In this paper, we examine two such products, Al-Urbun and Al-Istijrar, and determine fair prices for both the Al-Urbun and a class of Al-Istijrar under the Black–Scholes framework. Full article
(This article belongs to the Special Issue Financial Mathematics III)
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