Special Issue "Financial Mathematics II"

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

Deadline for manuscript submissions: closed (30 June 2022) | Viewed by 6169

Special Issue Editor

Prof. Dr. Antonella Basso
E-Mail Website
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 the last few years, financial mathematics has become an important field for mathematicians.

On the one hand, the development of mathematical and probabilistic models for finance have allowed to make progress in the classical fields of financial mathematics. Among these, we may cite criteria for the choice of the best alternative among investment or financing projects, and models for studying: The dynamics of interest rates, the evaluation of bonds, portfolio theory and dynamic asset allocation, the dynamics of stock prices, and the pricing and the risk assessment of many derivatives (options, forwards and futures, swaps, a variety of exotic derivatives).

On the other hand, other important issues have called for the formulation of mathematical models for studying new issues that have become relevant, sometimes hot, in financial markets. Especially the evaluation and management of the risks to which financial markets are exposed have become crucial. Thus, we find new models for the evaluation of credit risk of bonds and of bank loans, and models for the assessment of the sovereign risk.

In addition, new models to assess the performance of mutual funds makes use of different approaches drawn from different fields—among these data envelopment analysis—and allows to study socially-responsible investments.

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

This 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
  • interest rates dynamics
  • asset allocation
  • derivatives
  • credit risk
  • Sovereign risk
  • performance evaluation of mutual funds
  • socially responsible investments
  • data envelopment analysis

Published Papers (7 papers)

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Research

Article
Pension Funds, Insurance Companies and Stock Market Development: Evidence from Emerging Markets
Mathematics 2022, 10(13), 2335; https://doi.org/10.3390/math10132335 - 03 Jul 2022
Viewed by 577
Abstract
Stock markets foster economic growth through meeting the fund requirements of the firms by individual and institutional investors. Pension funds and insurance companies with their long-term investment horizon are critical institutional investors in capital markets. Therefore, this article explores the effect of pension [...] Read more.
Stock markets foster economic growth through meeting the fund requirements of the firms by individual and institutional investors. Pension funds and insurance companies with their long-term investment horizon are critical institutional investors in capital markets. Therefore, this article explores the effect of pension funds and insurance companies on stock market development in 15 emerging market economies over the 2004–2019 period through panel cointegration and causality tests. The causality analysis revealed that stock market development had a significant impact on pension funds and the insurance sector in the short term. However, the cointegration analysis revealed that pension funds had a positive effect on stock market development in Brazil, Chile, Hungary, Mexico, Peru, and South Africa and the insurance sector had a positive impact on stock market development in Chile, Indonesia, Korea Republic, Philippines, and South Africa in the long term. Full article
(This article belongs to the Special Issue Financial Mathematics II)
Article
A Positivity-Preserving Improved Nonstandard Finite Difference Method to Solve the Black-Scholes Equation
Mathematics 2022, 10(11), 1846; https://doi.org/10.3390/math10111846 - 27 May 2022
Viewed by 496
Abstract
In this paper, we evaluate and discuss different numerical methods to solve the Black–Scholes equation, including the θ-method, the mixed method, the Richardson method, the Du Fort and Frankel method, and the MADE (modified alternating directional explicit) method. These methods produce numerical [...] Read more.
In this paper, we evaluate and discuss different numerical methods to solve the Black–Scholes equation, including the θ-method, the mixed method, the Richardson method, the Du Fort and Frankel method, and the MADE (modified alternating directional explicit) method. These methods produce numerical drawbacks such as spurious oscillations and negative values in the solution when the volatility is much smaller than the interest rate. The MADE method sacrifices accuracy to obtain stability for the numerical solution of the Black–Scholes equation. In the present work, we improve the MADE scheme by using non-standard finite difference discretization techniques in which we use a non-local approximation for the reaction term (we call it the MMADE method). We will discuss the sufficient conditions to be positive of the new scheme. Also, we show that the proposed method is free of spurious oscillations even in the presence of discontinuous initial conditions. To demonstrate how efficient the new scheme is, some numerical experiments are performed at the end. Full article
(This article belongs to the Special Issue Financial Mathematics II)
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Article
Analytic Approximation for American Straddle Options
Mathematics 2022, 10(9), 1401; https://doi.org/10.3390/math10091401 - 22 Apr 2022
Viewed by 386
Abstract
This paper looks at adapting a recent approach found in the literature for pricing short-term American options to price American straddle options with two free boundaries. We provide a series solution in which explicit formulas for the coefficients are given. Hence, no complicated, [...] Read more.
This paper looks at adapting a recent approach found in the literature for pricing short-term American options to price American straddle options with two free boundaries. We provide a series solution in which explicit formulas for the coefficients are given. Hence, no complicated, recursive systems or nonlinear integral equations need to be solved, and the method efficiently provides fast solutions. We also compare the method with a numerical method and find that it gives very accurate prices not only for the option value, but also for the critical stock prices. Full article
(This article belongs to the Special Issue Financial Mathematics II)
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Article
Performance Evaluation of Fishery Enterprises Using Data Envelopment Analysis—A Malmquist Model
Mathematics 2021, 9(5), 469; https://doi.org/10.3390/math9050469 - 25 Feb 2021
Cited by 12 | Viewed by 1258
Abstract
In Vietnam, fishing is a crucial source of nutrition and employment, which not only affects the development of the domestic economy but is also closely related to exports, heavily influencing the economy and foreign exchange. However, the Vietnamese fishery sector has been facing [...] Read more.
In Vietnam, fishing is a crucial source of nutrition and employment, which not only affects the development of the domestic economy but is also closely related to exports, heavily influencing the economy and foreign exchange. However, the Vietnamese fishery sector has been facing many challenges in innovating production technology, improving product quality, and expanding markets. Hence, the fishery enterprises need to find solutions to increase labor productivity and enhance competitiveness while minimizing difficulties. This study implemented a performance evaluation from 2015 to 2018 of 17 fishery businesses, in decision making units (DMUs), in Vietnam by applying data envelopment analysis, namely the Malmquist model. The objective of the paper is to provide a general overview of the fishery sector in Vietnam through technical efficiency, technological progress, and the total factor productivity in the four-year period. The variables used in the model include total assets, equity, total liabilities, cost of sales, revenue, and profit. The results of the paper show that Investment Commerce Fisheries Corporation (DMU10) and Hoang Long Group (DMU8) exhibited the best performances. This paper offers a valuable reference to improve the business efficiency of Vietnamese fishery enterprises and could be a useful reference for related industries. Full article
(This article belongs to the Special Issue Financial Mathematics II)
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Article
Life Insurance and Subsistence Consumption with an Exponential Utility
Mathematics 2021, 9(4), 358; https://doi.org/10.3390/math9040358 - 11 Feb 2021
Cited by 1 | Viewed by 690
Abstract
In this paper, we derive an explicit solution to the utility maximization problem of an individual with mortality risk and subsistence consumption constraint. We adopt an exponential utility for the individual’s consumption and the martingale and duality method is employed. From the explicit [...] Read more.
In this paper, we derive an explicit solution to the utility maximization problem of an individual with mortality risk and subsistence consumption constraint. We adopt an exponential utility for the individual’s consumption and the martingale and duality method is employed. From the explicit solution, we exhibit how the mortality intensity and subsistence consumption constraint affect, separately and together, portfolio, consumption and life insurance purchase. Full article
(This article belongs to the Special Issue Financial Mathematics II)
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Article
Valuation of Exchange Option with Credit Risk in a Hybrid Model
Mathematics 2020, 8(11), 2091; https://doi.org/10.3390/math8112091 - 23 Nov 2020
Cited by 2 | Viewed by 766
Abstract
In this paper, the valuation of the exchange option with credit risk under a hybrid credit risk model is investigated. In order to build the hybrid model, we consider both the reduced-form model and the structural model. We adopt the probabilistic approach to [...] Read more.
In this paper, the valuation of the exchange option with credit risk under a hybrid credit risk model is investigated. In order to build the hybrid model, we consider both the reduced-form model and the structural model. We adopt the probabilistic approach to derive the closed-form formula of an exchange option price with credit risk under the proposed model. Specifically, the change of measure technique is used repeatedly, and the pricing formula is provided as the standard normal cumulative distribution functions. Full article
(This article belongs to the Special Issue Financial Mathematics II)
Article
DEA-BSC and Diamond Performance to Support Museum Management
Mathematics 2020, 8(9), 1402; https://doi.org/10.3390/math8091402 - 21 Aug 2020
Viewed by 1055
Abstract
In the present paper, we propose some models for the computation of an overall indicator which measures the performance of a set of museums from a multidimensional point of view. One of the most used methodologies that provide a multiple input–multiple output performance [...] Read more.
In the present paper, we propose some models for the computation of an overall indicator which measures the performance of a set of museums from a multidimensional point of view. One of the most used methodologies that provide a multiple input–multiple output performance score is Data Envelopment Analysis (DEA), which in recent years has also been applied to museums. Recently, the literature on museums performance has proposed a model that combines DEA with the Balanced Scorecard (BSC) approach, which is used in the management control of organisations and focuses on a multidimensional framework based on four different dimensions of the organisation management. In the present contribution, we propose a two-stage DEA-BSC model which adopts more plain DEA models without weight restrictions and can be better understood by museums’ managers. In addition, in order to overcome the drawback of the low discriminatory power shown by this model when applied to a few museums, we propose some alternative ways to compute the overall performance at the second stage. One indicator computes the area of a special geometric representation of the efficiency scores obtained at the first stage for the four BSC perspectives and for this reason is named diamond efficiency. Finally, the models proposed are applied to the set of municipal museums of Venice. Full article
(This article belongs to the Special Issue Financial Mathematics II)
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