Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
5.0
1.5
Journals
Risks
Special Issues
Mathematical Methods Applied in Pricing and Investment Problems
share announcement

Mathematical Methods Applied in Pricing and Investment Problems

A special issue of Risks (ISSN 2227-9091).

Deadline for manuscript submissions: closed (30 November 2025) | Viewed by 7488

Special Issue Editors

Dr. Traian A Pirvu

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada
Interests: optimal investment and pricing in incomplete markets; equilibrium pricing of non-tradable risks; optimal portfolio selection with regulatory constraints; time consistent portfolio management; prospect theory
Special Issues, Collections and Topics in MDPI journals
Dr. Petar Jevtic

E-Mail Website
Co-Guest Editor
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
Interests: risk management; actuarial science; mathematical finance; longevity risk; property and casualty insurance; cyber risk; the burgeoning field of risks associated with smart contracts and autonomous systems; risks induced by climate change
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Many financial and insurance products are based on risk factors, and are not directly traded. The pricing of these products is sometimes linked to optimal investment in financial and insurance markets. One such example of this is from Jevtić, Kwak, and Pirvu (2022) who developed a continuous time model for the optimal investment and pricing of mortality-linked instruments.

In this Special Issue, we are aiming to collect high-quality research papers focusing on the mathematical modelling and methodology of pricing non-tradable risks, and optimal investment in financial and insurance markets. You are invited to submit your research on continuous time stochastic models and methods for pricing non-tradable risks, and stochastic optimal control problems in finance and insurance, modelling optimal investment.

Dr. Traian A Pirvu
Guest Editor

Dr. Petar Jevtic
Co-Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Risks is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • non-tradable risk
  • longevity risk
  • climate risk
  • cyber risk
  • optimal investment
  • insurance mathematics
  • financial mathematics

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

38 pages, 1971 KB  
Article
Guaranteed Annuity Option Under Correlated and Regime-Switching Risks
by Jude Martin B. Grozen and Rogemar S. Mamon
Risks 2026, 14(2), 42; https://doi.org/10.3390/risks14020042 - 23 Feb 2026
Viewed by 1086
Abstract
Guaranteed annuity options (GAOs) allow policyholders to convert accumulated funds into life annuities at maturity at a guaranteed minimum rate. Thus, insurers are exposed to both investment and longevity risks. Accurate valuation of these long-term, survival-contingent contracts is essential for solvency assessment and [...] Read more.
Guaranteed annuity options (GAOs) allow policyholders to convert accumulated funds into life annuities at maturity at a guaranteed minimum rate. Thus, insurers are exposed to both investment and longevity risks. Accurate valuation of these long-term, survival-contingent contracts is essential for solvency assessment and risk management. Many existing approaches assume independence between interest rate and mortality risks. This paper develops a computationally efficient pricing framework for GAOs that jointly models interest and mortality rates as correlated stochastic processes with regime-switching dynamics governed by a finite-state continuous-time Markov chain. Model parameters are estimated using U.S. interest rates and cohort mortality data via quasi-maximum likelihood estimation. A semi-analytic valuation formula is derived based on the joint distribution of the underlying processes. Numerical results show that incorporating correlation and regime-switching materially increases GAO prices relative to conventional one-state models. The proposed semi-analytic approach delivers substantial computational advantages over standard Monte Carlo simulations. Sensitivity analysis further identifies the parameters most relevant for long-horizon pricing and solvency considerations. This highlights the practical relevance of the framework for managing longevity-linked guarantees under economic and demographic uncertainty. Full article
(This article belongs to the Special Issue Mathematical Methods Applied in Pricing and Investment Problems)
►▼ Show Figures

Figure 1

18 pages, 1720 KB  
Article
Robust Portfolio Optimization in Crypto Markets Using Second-Order Tsallis Entropy and Liquidity-Aware Diversification
by Florentin Șerban and Silvia Dedu
Risks 2025, 13(9), 180; https://doi.org/10.3390/risks13090180 - 17 Sep 2025
Viewed by 2388
Abstract
In this paper, we propose a novel optimization model for portfolio selection that integrates the classical mean–variance criterion with a second-order Tsallis entropy term. This approach enables a trade-off between expected return, risk, and diversification, extending Markowitz’s theory to account for non-Gaussian characteristics [...] Read more.
In this paper, we propose a novel optimization model for portfolio selection that integrates the classical mean–variance criterion with a second-order Tsallis entropy term. This approach enables a trade-off between expected return, risk, and diversification, extending Markowitz’s theory to account for non-Gaussian characteristics and heavy-tailed distributions that are typical in financial markets—especially in cryptocurrency assets. Unlike the first-order Tsallis entropy, the second-order version amplifies the effects of distributional structure and allows for more refined penalization of portfolio concentration. We derive the analytical solution for the optimal weights under this extended framework and demonstrate its performance through a case study using real data from selected cryptocurrencies. Efficient frontiers, portfolio weights, and entropy indicators are compared across models. This novel combination may improve portfolio selection under uncertainty, especially in the context of volatile assets such as cryptocurrencies, as the proposed model can provide a more robust and diversified portfolio structure compared to conventional theories. Full article
(This article belongs to the Special Issue Mathematical Methods Applied in Pricing and Investment Problems)
►▼ Show Figures

Figure 1

14 pages, 644 KB  
Article
Spread Option Pricing Under Finite Liquidity Framework
by Traian A. Pirvu and Shuming Zhang
Risks 2024, 12(11), 173; https://doi.org/10.3390/risks12110173 - 31 Oct 2024
Cited by 2 | Viewed by 2607
Abstract
This work explores a finite liquidity model to price spread options and assess the liquidity impact. We employ Kirk approximation for computing the spread option price and its delta. The latter is needed since the liquidity impact is caused by the delta hedging [...] Read more.
This work explores a finite liquidity model to price spread options and assess the liquidity impact. We employ Kirk approximation for computing the spread option price and its delta. The latter is needed since the liquidity impact is caused by the delta hedging of a large investor. Our main contribution is a novel methodology to price spread options in this paradigm. Kirk approximation in conjunction with Monte Carlo simulations yields the spread option prices. Moreover, the antithetic and control variates variance reduction techniques improve the performance of our method. Numerical experiments reveal that the finite liquidity causes a liquidity value adjustment in option prices ranging from 0.53% to 2.81%. The effect of correlation on prices is also explored, and as expected the option price increases due to the diversification effect, but the liquidity impact decreases slightly. Full article
(This article belongs to the Special Issue Mathematical Methods Applied in Pricing and Investment Problems)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop