Stochastic Analysis and Applications in Financial Mathematics

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

Deadline for manuscript submissions: 30 April 2024 | Viewed by 2143

Special Issue Editors


E-Mail Website
Guest Editor
Centre for Industrial and Applied Mathematics, UniSA STEM, University of South Australia, Adelaide 5001, Australia
Interests: stochastic processes; mathematical finance; non-parametric estimation; approximation theory

E-Mail Website
Guest Editor
School of Mathematical and Physical Sciences, University of Technology Sydney, Sydney 2007, Australia
Interests: mortality and longevity risk modelling; actuarial mathematics; financial mathematics; option pricing; stochastic calculus

Special Issue Information

Dear Colleagues,

The origin of the application of rigorous mathematical and stochastic methods for asset pricing can be traced back to Louis Bachelier’s 1900 doctoral thesis Théorie de la spéculation. From the early 1950s, economists, including Paul Samuelson, started to model asset prices using geometric Brownian motion. The Black and Scholes paper in 1973 is the first to show that the European option price is the solution of a partial differential equation that is derived from a self-financing hedging argument, which is also followed by some extensions by Merton in 1973. Merton, in 1976, further extended the Samuelson–Black–Scholes geometric Brownian motion asset pricing model to a geometric jump-diffusion model and derived a pricing formula for a European call option under a jump-diffusion model. Margrabe, in 1978, extended the Black–Scholes call/put option pricing formula under geometric Brownian motion dynamics to price a European-style exchange option. This was an early example of pricing an option written on multiple assets, which was extended by Carmona and Durrleman, in 2003, to more general spread options. The work by Harrison and Pliska, in 1981, also formalised the relationship between risk-neutral valuation and equivalent martingale measures, which also led to the Fundamental Theorems of Asset Pricing by Delbaen and Schachermayer in 1994. The original Black–Scholes 1973 model was also extended to include stochastic volatility (e.g., Hull and White in 1987 and Heston in 1993), both stochastic volatility and jumps (e.g., Bates in 1996). Other option pricing models that have been introduced include the Variance–Gamma model by Madan and Seneta in 1990 and Hidden Markov models by Elliott et al. in 1995. Apart from option pricing models, there is also a wealth of literature on interest rate term structure models and option pricing with stochastic interest rates.

In addition to stochastic analysis in asset pricing, option and derivatives pricing, and interest rate modelling, techniques around stochastic optimal control, forward–backward stochastic differential equations (FBSDEs), and stochastic filtering, among others, have gained greater traction in addressing financial problems, such as portfolio management and optimization, risk management and measurement, algorithmic trading and trading strategies, among many other areas of application.

In this Special Issue, we call for original papers that further extend the frontiers of the existing rich literature, as well as shorter insightful review and survey papers on the applications of stochastic analysis in financial mathematics.

Dr. Gerald H. L. Cheang
Dr. Len Patrick Garces
Guest Editors

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 100 words) can be sent to the Editorial Office for announcement on this website.

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • financial mathematics
  • stochastic analysis
  • stochastic optimal control
  • asset pricing

Published Papers (2 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

11 pages, 285 KiB  
Article
Valuation of Commodity-Linked Bond with Stochastic Convenience Yield, Stochastic Volatility, and Credit Risk in an Intensity-Based Model
by Junkee Jeon and Geonwoo Kim
Mathematics 2023, 11(24), 4969; https://doi.org/10.3390/math11244969 - 15 Dec 2023
Cited by 1 | Viewed by 560
Abstract
In this study, we consider an intensity-based model for pricing a commodity-linked bond with credit risk. Recently, the pricing of a commodity-linked bond with credit risk under the structural model has been studied. We extend the result using an intensity-based model, stochastic volatility [...] Read more.
In this study, we consider an intensity-based model for pricing a commodity-linked bond with credit risk. Recently, the pricing of a commodity-linked bond with credit risk under the structural model has been studied. We extend the result using an intensity-based model, stochastic volatility model, and stochastic convenience yield model. In the intensity-based model, the credit event by the counterparty occurs at the time of first jump in a stochastic Poisson process, in which intensity is modeled as the sum of two CIR prosesses. We assume that the underlying asset follows the stochastic volatility and convenience yield models. Using the measure change technique, we explicitly derive the commodity-linked bond pricing formula in the proposed model. As a result, we provide the explicit solution for the price of the commodity-linked bond with stochastic convenience yield, stochastic volatility, and credit risk as single integrations. In addition, we present several examples to demonstrate the effects of significant parameters on the value of commodity-linked bond using numerical integration. In particular, examples are provided, focusing on the behavior of prices based on effects of recovery rate. Full article
(This article belongs to the Special Issue Stochastic Analysis and Applications in Financial Mathematics)
Show Figures

Figure 1

20 pages, 331 KiB  
Article
A Stochastic Control Approach for Constrained Stochastic Differential Games with Jumps and Regimes
by Emel Savku
Mathematics 2023, 11(14), 3043; https://doi.org/10.3390/math11143043 - 09 Jul 2023
Cited by 3 | Viewed by 957
Abstract
We develop an approach for two-player constraint zero-sum and nonzero-sum stochastic differential games, which are modeled by Markov regime-switching jump-diffusion processes. We provide the relations between a usual stochastic optimal control setting and a Lagrangian method. In this context, we prove corresponding theorems [...] Read more.
We develop an approach for two-player constraint zero-sum and nonzero-sum stochastic differential games, which are modeled by Markov regime-switching jump-diffusion processes. We provide the relations between a usual stochastic optimal control setting and a Lagrangian method. In this context, we prove corresponding theorems for two different types of constraints, which lead us to find real-valued and stochastic Lagrange multipliers, respectively. Then, we illustrate our results for a nonzero-sum game problem with the stochastic maximum principle technique. Our application is an example of cooperation between a bank and an insurance company, which is a popular, well-known business agreement type called Bancassurance. Full article
(This article belongs to the Special Issue Stochastic Analysis and Applications in Financial Mathematics)
Back to TopTop