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Full-Text Articles in Analysis
On The Existence, Uniqueness And Stability Of Solutions Of Sdes With State-Dependent Variable Exponent, Mustafa Avci
On The Existence, Uniqueness And Stability Of Solutions Of Sdes With State-Dependent Variable Exponent, Mustafa Avci
Journal of Stochastic Analysis
We study a time-inhomogeneous nonlinear SDE with drift and diffusion governed by state-dependent variable exponents. This framework generalizes models like the geometric Brownian motion (GBM) and the constant elasticity of variance (CEV), offering flexibility to capture complex dynamics while posing analytical challenges. Using a fixed-point approach, we prove existence and uniqueness, analyze higher-order moments, derive asymptotic estimates, and assess stability. Finally, we illustrate an application where Poisson’s equation admits a probabilistic representation via a timehomogeneous nonlinear SDE with state-dependent variable exponents.
Companion Matrices Associated To Stochastic Matrices, Andreas Boukas, Philip Feinsilver
Companion Matrices Associated To Stochastic Matrices, Andreas Boukas, Philip Feinsilver
Journal of Stochastic Analysis
Starting with a stochastic matrix, we study the behavior of powers of an associated companion matrix, which has the same characteristic polynomial as the original matrix. In general the companion matrix will have negative entries while maintaining rowsums equal to 1. We will find the growth rate even if the Ces`aro limit of the sums of the companion matrix diverge. Surprisingly, in the irreducible aperiodic case the powers of the companion matrix will converge even though the norm of the matrix exceeds 1 and it has possibly negative entries.
Z+-Valued Additive Processes In Law With Nonnegative Increments, Nadjib Bouzar
Z+-Valued Additive Processes In Law With Nonnegative Increments, Nadjib Bouzar
Journal of Stochastic Analysis
The goal of this article is to study in depth the subclass of Z+- valued additive processes in law with nonnegative increments. We establish key distributional properties of these processes and obtain some existence results under a variety of conditions. We show that they form a subclass of the family of inhomogeneous Markov chains with spatial homogeneity. We extend the notion of factoring introduced by Sato (2004, [9]) for Rd-valued additive processes in law to their Z+-valued counterparts with nonnegative increments. We give a sufficient condition for the existence of a factoring for these processes. Lastly, we obtain their representation …
A Stochastic Maximum Principle For Singular Mean-Field Regime-Switching Optimal Control, Maalvladedon Ganet Some, Edward Korveh
A Stochastic Maximum Principle For Singular Mean-Field Regime-Switching Optimal Control, Maalvladedon Ganet Some, Edward Korveh
Journal of Stochastic Analysis
In this paper, we investigate a mean-field singular stochastic optimal control problem for systems governed by mean-field regime-switching singular stochastic differential equations. The state process is assumed to depend on both a regular and a singular control, and the coefficient associated with the singular component is allowed to be regime dependent. We derive both necessary and sufficient singular stochastic maximum principles. Because the regular control domain is not assumed to be convex, we employ the spike variation technique and obtain the necessary maximum principle by introducing a second-order adjoint process. As an application, we use the main theoretical results to …
Generalized Delayed Black–Scholes Formula, Bi Gole Hubert Le, Auguste Aman
Generalized Delayed Black–Scholes Formula, Bi Gole Hubert Le, Auguste Aman
Journal of Stochastic Analysis
The aim of this paper is to derive an explicit pricing formula for European options when the underlying asset follows a linear generalized delay differential equation in two distinct financial markets. The pricing methodology is based on the construction of an equivalent martingale measure using Girsanov’s theorem. Our models preserve both the no-arbitrage condition and market completeness. As such, this work extends the framework previously developed by Arriojas et al. in [16], providing a broader class of delay-based option pricing models.
Robust Optimal Consumption, Investment And Reinsurance For Recursive Preferences, Elizabeth Dadzie, Wilfried Kuissi Kamdem, Marcel Ndengo
Robust Optimal Consumption, Investment And Reinsurance For Recursive Preferences, Elizabeth Dadzie, Wilfried Kuissi Kamdem, Marcel Ndengo
Journal of Stochastic Analysis
This paper investigates a robust optimal consumption, investment, and reinsurance problem for an insurer with Epstein-Zin recursive preferences operating under model uncertainty. The insurer’s surplus follows the diffusion approximation of the Cramér-Lundberg model, and the insurer can purchase proportional reinsurance. Model ambiguity is characterised by a class of equivalent probability measures, and the insurer, being ambiguity-averse, aims to maximise utility under the worst-case scenario. By solving the associated coupled forward-backward stochastic differential equation (FBSDE), we derive closed-form solutions for the optimal strategies and the value function. Our analysis reveals how ambiguity aversion, risk aversion, and the elasticity of intertemporal substitution …
An Itô Integral For A Two-Sided Lévy Process, Raluca Balan, Jaime Garza
An Itô Integral For A Two-Sided Lévy Process, Raluca Balan, Jaime Garza
Journal of Stochastic Analysis
In this article, we construct an Itô integral with respect to a two-sided finite-variance Lévy process {L(x)}x∈R, without a Gaussian component. Using Rosenthal inequality for discrete-time martingales, we give an estimate for the p-th moment of this integral, for any even integer p ≥ 2. Then, using Poisson-Malliavin calculus, we show that the Itô integral is an extension of the Hitsuda-Skorokhod integral with respect to the compensated Poisson random measure associated to the Lévy process.
Supersymmetric Quantum Fields Via Quantum Probability, Radhakrishnan Balu
Supersymmetric Quantum Fields Via Quantum Probability, Radhakrishnan Balu
Journal of Stochastic Analysis
The super version of imprimitivity theorem is available now to describe global supersymmetry of systems using the representations of super Lie groups (SLG). This result uses the equivalence between super Harish- Chandra pairs and super Lie groups, at the categorical level, and is applicable to super Poincaré group and generalizes a smooth SI to super context. We apply the result to build supersymmetric quantum fields. Towards this end, we set up a super Fock space of a disjoint union of super Hilbert spaces which is equivalent to super tensoring of boson (even) part symmetrically and that of fermion (odd) part …
Convergence To Fractional Brownian Motion For Weighted Random Sums In Besov Space, Ibrahima Mendy
Convergence To Fractional Brownian Motion For Weighted Random Sums In Besov Space, Ibrahima Mendy
Journal of Stochastic Analysis
We consider infinite sums of weighted i.i.d. random variables, with finite variance and arbitrary distribution, and we derives conditions for the weak convergence in Besov space of normalized sums to fractional Brownian motion (fBm).
Pricing Variance Swaps Using Extended Heston Model, Semere Gebresilasie, Mulue Gebreslasie, Indranil Sengupta
Pricing Variance Swaps Using Extended Heston Model, Semere Gebresilasie, Mulue Gebreslasie, Indranil Sengupta
Journal of Stochastic Analysis
Abstract. In this study, we introduce a variance swap for the underlying asset utilizing the Heston model, incorporating a long-term variance that is treated as a stochastic function of time. We develop a closed-form solution for the variance swap under this framework, where the log returns are driven by a compound Poisson process. Our analysis of historical data reveals that long-term variance is not constant; instead, it fluctuates over time, reflecting market dynamics more accurately. By integrating this time-varying long-term variance into the model, we achieve an improvement in prediction performance of approximately 60%. Furthermore, we perform model calibration using …
Minimal Supersolution Of Bsdes Driven By Continuous Martingales In A General Filtration, Badr Elmansouri, Mohamed El Otmani
Minimal Supersolution Of Bsdes Driven By Continuous Martingales In A General Filtration, Badr Elmansouri, Mohamed El Otmani
Journal of Stochastic Analysis
In this paper, we study minimal supersolutions of backward stochastic differential equations (BSDEs) driven by a continuous local martingale in a general filtration. We establish existence, uniqueness, and stability results under various mild conditions on the terminal value and the generator. Additionally, we explore the connection between the concept of non-linear expectation and minimal supersolutions, emphasizing the specific properties that are relevant to our framework. We also prove a general monotonic limit theorem and apply this result to determine the smallest constrained supersolution of a BSDE with a possibly non-convex constraint.
Arbitrage-Free Pricing With Diffusion-Dependent Jumps, Hamza A. Virk, Yihren Wu, Majnu John
Arbitrage-Free Pricing With Diffusion-Dependent Jumps, Hamza A. Virk, Yihren Wu, Majnu John
Journal of Stochastic Analysis
Standard jump-diffusion models assume independence between jumps and diffusion components. We develop a multi-type jump-diffusion model where jump occurrence and magnitude depend on contemporaneous diffusion movements. Unlike previous one-sided models that create arbitrage opportunities, our framework includes upward and downward jumps triggered by both large upward and large downward diffusion increments. We derive the explicit no-arbitrage condition linking the physical drift to model pa- rameters and market risk premia by constructing an Equivalent Martingale Measure using Girsanov’s theorem and a normalized Esscher transform. This condition provides a rigorous foundation for arbitrage-free pricing in models with diffusion-dependent jumps.
A Bdg Inequality For Stochastic Volterra Integrals, Alexandre Pannier
A Bdg Inequality For Stochastic Volterra Integrals, Alexandre Pannier
Journal of Stochastic Analysis
We establish Burkholder-Davis-Gundy-type inequalities for stochastic Volterra integrals with a completely monotone convolution kernel, which may exhibit singular behaviour at the origin. When the supremum is taken over a finite interval, the upper bound depends linearly on the Lγ-norm of the kernel, for any γ > 2. We demonstrate the utility of this inequality in quantifying the pathwise distance between two stochastic Volterra equations with distinct kernels, with a particular emphasis on the multifactor Markovian approximation. For kernels that decay sufficiently fast, we derive an alternative inequality valid over an infinite time interval, providing uniformin- time bounds for mean-reverting stochastic Volterra …
The Characteristic Function Of The Cube Of A Gaussian Random Variable, Andreas Boukas
The Characteristic Function Of The Cube Of A Gaussian Random Variable, Andreas Boukas
Journal of Stochastic Analysis
Using the spectral resolution of the multiplication operator on the Schwartz class of L2(R,C), we compute the characteristic function of the cube of a Gaussian random variable.
Operator Information Quantities Of Semigroups Associated With Functions Of The Number Operator, Ryo Inayoshi, Kimiaki Saito
Operator Information Quantities Of Semigroups Associated With Functions Of The Number Operator, Ryo Inayoshi, Kimiaki Saito
Journal of Stochastic Analysis
In this paper, we present recent developments on the operator information quantity acting on white noise functionals. In particular, we give a stochastic expression of the operator information quantity of a semigroup generated by some function of the number operator through a white noise delta distribution centered at an infinite dimensional Ornstein-Uhlenbeck process.
On Excursions Associated With A Certain Local Time Of Simple Symmetric Random Walks, With Applications, Takahiko Fujita, Naohiro Yoshida
On Excursions Associated With A Certain Local Time Of Simple Symmetric Random Walks, With Applications, Takahiko Fujita, Naohiro Yoshida
Journal of Stochastic Analysis
In this note, some applications of excursions associated with a certain local time of simple symmetric random walks are presented. Specifically, the excursions are applied to calculate some probability distributions of interest regarding the random walks. Furthermore, a solution of the Skorokhod embedding problem for random walks is obtained through the excursions.
The Jacod-Yor Theorem For Sigma Martingales And The Second Fundamental, Moritz Sohns
The Jacod-Yor Theorem For Sigma Martingales And The Second Fundamental, Moritz Sohns
Journal of Stochastic Analysis
In this paper, we prove the Jacod-Yor Theorem for sigma martingales, a class of processes that generalize local martingales and play a pivotal role in financial mathematics. While the Jacod-Yor Theorem has been extensively studied for L2-martingales, martingales, and local martingales, no prior version exists for sigma martingales. Our result establishes the connection between sigma martingales and their martingale representation properties, addressing a critical gap in the literature. As an application, we prove the Second Fundamental Theorem of Asset Pricing for markets where price processes are modeled as sigma martingales.
My Tunisia Encounters: Inspiration For Some Mathematical Ideas, Hui-Hsiung Kuo
My Tunisia Encounters: Inspiration For Some Mathematical Ideas, Hui-Hsiung Kuo
Journal of Stochastic Analysis
No abstract provided.
Gaussian Quantum Markov Semigroups In The Fock-Anti-Fock Representation Of Weyl Algebra, A Dhahri, Franco Fagnola, D Poletti, Hyun Jae Yoo
Gaussian Quantum Markov Semigroups In The Fock-Anti-Fock Representation Of Weyl Algebra, A Dhahri, Franco Fagnola, D Poletti, Hyun Jae Yoo
Journal of Stochastic Analysis
No abstract provided.
Stochastic Analysis And White Noise Calculus Of Nonlinear Wave Equations With Application To Laser Generation And Propagation, Sivaguru S. Sritharan, Saba Mudaliar
Stochastic Analysis And White Noise Calculus Of Nonlinear Wave Equations With Application To Laser Generation And Propagation, Sivaguru S. Sritharan, Saba Mudaliar
Journal of Stochastic Analysis
No abstract provided.
An Operator Information Quantity Of A Semigroup And Associated Differential Equations, Kimiaki Saito, Ryo Inayoshi
An Operator Information Quantity Of A Semigroup And Associated Differential Equations, Kimiaki Saito, Ryo Inayoshi
Journal of Stochastic Analysis
No abstract provided.
The Product Formula Of Multiple Stochastic Integrals With Respect To The Poisson Space Noise, Yuh-Jia Lee, Hsin-Hung Shih
The Product Formula Of Multiple Stochastic Integrals With Respect To The Poisson Space Noise, Yuh-Jia Lee, Hsin-Hung Shih
Journal of Stochastic Analysis
No abstract provided.
American Option Pricing Using Generalised Stochastic Hybrid Systems, Evelyn Buckwar, Sascha Desmettre, Agnes Mallinger, Amira Meddah
American Option Pricing Using Generalised Stochastic Hybrid Systems, Evelyn Buckwar, Sascha Desmettre, Agnes Mallinger, Amira Meddah
Journal of Stochastic Analysis
No abstract provided.
About Fixed Points Of Quantum Channels, Raffaella Carbone
About Fixed Points Of Quantum Channels, Raffaella Carbone
Journal of Stochastic Analysis
No abstract provided.
Ornstein-Uhlenbeck Type Operators Induced By Some Geometric Structures On Complex Domains, Souheyl Jendoubu
Ornstein-Uhlenbeck Type Operators Induced By Some Geometric Structures On Complex Domains, Souheyl Jendoubu
Journal of Stochastic Analysis
No abstract provided.
Quantum Extensions Of The Exotic Laplacians And Associated Quantum Heat Semigroups, Luigi Accardi, Un Cig Ji, Kimiaki Saito
Quantum Extensions Of The Exotic Laplacians And Associated Quantum Heat Semigroups, Luigi Accardi, Un Cig Ji, Kimiaki Saito
Journal of Stochastic Analysis
No abstract provided.
Preface, José Luis Da Silva, Un Cig Ji, Aurel Stan
Preface, José Luis Da Silva, Un Cig Ji, Aurel Stan
Journal of Stochastic Analysis
No abstract provided.
Weak Solutions Of Spdes In The Space Of Tempered Distributions, Suprio Bhar, Barun Sarkar
Weak Solutions Of Spdes In The Space Of Tempered Distributions, Suprio Bhar, Barun Sarkar
Journal of Stochastic Analysis
No abstract provided.
A Family Of Markov Chains, Schur Functions, And Exterior Powers, Philip Feinsilver, John P. Mcsorley
A Family Of Markov Chains, Schur Functions, And Exterior Powers, Philip Feinsilver, John P. Mcsorley
Journal of Stochastic Analysis
No abstract provided.
On An Asset Model Of Merton Type: Long-Term Observations In Financial Time-Series, Shuya Kanagawa, Narn-Rueih Shieh
On An Asset Model Of Merton Type: Long-Term Observations In Financial Time-Series, Shuya Kanagawa, Narn-Rueih Shieh
Journal of Stochastic Analysis
No abstract provided.