Mathematical Methods Applied in Pricing and Investment Problems

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

Deadline for manuscript submissions: 31 March 2025 | Viewed by 1082

Special Issue Editors


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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
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Co-Guest Editor
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, 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; and 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

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Keywords

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

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Published Papers (1 paper)

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Research

14 pages, 644 KiB  
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
Viewed by 628
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)
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