Recent Advances in Stochastic Processes and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 29 January 2027 | Viewed by 1249

Special Issue Editor


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Guest Editor
Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, ON N6A 3K7, Canada
Interests: stochastic processes; financial mathematics; statistics

Special Issue Information

Dear Colleagues,

Stochastic processes permeate many scientific disciplines, from economics and finance within social sciences, biology and physics in natural sciences, to actuarial, computer, data, and system sciences. The area is also a discipline on its own with frequent advances in terms of new processes, conditions for existence and uniqueness, and analytical solutions motivated by applications. The richness and interaction of its continuous and discrete-time branches, together with the explosion of data and machine learning techniques, make it an ideal candidate to generate innovation. 

Given such a wide range of theory and applications, this Special Issue focuses on the innovative use of stochastic processes motivated, at least partially, by challenges in economics, insurance, and finance. Priority will be given to the combination of stochastic processes with statistical and machine learning methodologies, such as estimation, reinforcement learning, decision trees, and artificial neural networks.

We look forward to receiving your contributions.

Prof. Dr. Marcos Escobar-Anel
Guest Editor

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Keywords

  • stochastic covariance
  • mathematical finance
  • mathematical insurance
  • continuous-time process
  • discrete-time process
  • financial portfolio management
  • fractional processes
  • exotic derivative pricing

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Published Papers (3 papers)

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Research

23 pages, 439 KB  
Article
Semi-Analytical Pricing of Barrier Options in a Hybrid Model of Stochastic and Local Volatility
by Jiling Cao, Sheng Gong, Xi Li and Wenjun Zhang
Mathematics 2026, 14(10), 1651; https://doi.org/10.3390/math14101651 - 13 May 2026
Viewed by 199
Abstract
In this paper, the valuation of barrier options is studied when the underlying asset is driven by a hybrid model of stochastic volatility and constant elasticity of variance. Using an asymptotic expansion approach and the Fourier transform method, a semi-analytical approximate pricing formula [...] Read more.
In this paper, the valuation of barrier options is studied when the underlying asset is driven by a hybrid model of stochastic volatility and constant elasticity of variance. Using an asymptotic expansion approach and the Fourier transform method, a semi-analytical approximate pricing formula for up-and-out call options are derived under the proposed hybrid model. We validate the approximate pricing formula by comparing its outputs with those produced by Monte Carlo simulation and the binomial tree method. In addition, we perform a sensitivity analysis numerically on the key model parameters and investigate limiting regimes of the hybrid model. It is verified that the approximation is properly anchored to simpler benchmark models when one or both perturbative effects vanish. Full article
(This article belongs to the Special Issue Recent Advances in Stochastic Processes and Their Applications)
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40 pages, 985 KB  
Article
Optimal Consumption and Investment with Consumption Comfort Zones
by Geonwoo Kim and Junkee Jeon
Mathematics 2026, 14(9), 1523; https://doi.org/10.3390/math14091523 - 30 Apr 2026
Viewed by 263
Abstract
We study an infinite-horizon consumption–investment problem in which an investor endogenously manages a consumption comfort zone above a fixed subsistence benchmark. Consumption can move freely within the prevailing admissible interval, while upward expansions of the upper endpoint are irreversible and costly. This captures [...] Read more.
We study an infinite-horizon consumption–investment problem in which an investor endogenously manages a consumption comfort zone above a fixed subsistence benchmark. Consumption can move freely within the prevailing admissible interval, while upward expansions of the upper endpoint are irreversible and costly. This captures downward rigidity not through a single ratcheting reference level but through the endogenous management of a sustainable expenditure range. Using the dual martingale method together with singular stochastic control, we reduce the problem to a one-sided singular control problem for the comfort-zone width process. The associated dual Hamilton–Jacobi–Bellman equation becomes a gradient-constrained free-boundary problem, which admits a one-dimensional reduction under CRRA utility. We characterize the optimal comfort-zone expansion rule, consumption policy, risky portfolio rule, and value function. Economically, the model implies infrequent upward revisions of the sustainable consumption ceiling, smoother consumption than in the frictionless Merton benchmark, and state-dependent portfolio behavior. A key implication of the additive specification is that proportional consumption flexibility shrinks as the upper endpoint rises, so higher consumption states become endogenously tighter and require a larger wealth buffer to sustain. The infinite-horizon formulation is interpreted as a stationary benchmark that isolates the economics of costly lifestyle upgrading. Full article
(This article belongs to the Special Issue Recent Advances in Stochastic Processes and Their Applications)
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53 pages, 1515 KB  
Article
Agent-Based Models for Two Stocks with Superhedging
by Dario Crisci, Sebastian Ferrando and Konrad Gajewski
Mathematics 2026, 14(6), 968; https://doi.org/10.3390/math14060968 - 12 Mar 2026
Viewed by 321
Abstract
We propose an agent-based, non-probabilistic framework for modeling the joint evolution of two discounted asset prices expressed in units of a third asset acting as numeraire. The framework is based on a trajectorial superhedging theory, in which pricing, arbitrage, and null events are [...] Read more.
We propose an agent-based, non-probabilistic framework for modeling the joint evolution of two discounted asset prices expressed in units of a third asset acting as numeraire. The framework is based on a trajectorial superhedging theory, in which pricing, arbitrage, and null events are defined purely in financial terms, without reference to probability measures or martingale assumptions. A central necessary theoretical requirement is that the global property (L)-a.e. holds, ensuring consistency of the model construction. Admissible price evolutions are described by multidimensional trajectory sets generated from observable price movements and operational rebalancing rules representing a prescribed class of agents. Within a fixed trajectory set, relative price bounds between the two assets are obtained via superhedging and subhedging by means of self-financing portfolios that trade one asset against the other. Full article
(This article belongs to the Special Issue Recent Advances in Stochastic Processes and Their Applications)
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