Regularity of weak solutions to a class of fourth order parabolic variational inequality problems arising from swap option pricing

Article Mathematics, Applied

Some results for a variation-inequality problem with fourth order p(x)-Kirchhoff operator arising from options on fresh agricultural products

Tao Wu

Summary: In this paper, we investigate variation-inequality initial-boundary value problems with fourth-order p(x)-Kirchhoff operators. Firstly, an operator is constructed using the Leray Schauder principle, and the existence of solutions is proven. Secondly, the stability and uniqueness of the solution are analyzed by appropriately relaxing the conditions on the Kirchhoff operators.

AIMS MATHEMATICS (2023)

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Article Mathematics, Applied

Well-posedness for multi-time variational inequality problems via generalized monotonicity and for variational problems with multi-time variational inequality constraints

Shalini Jha et al.

Summary: This paper investigates the well-posedness of multi-time variational inequality problems and the corresponding variational problems. By introducing the multi-time variational inequality problems determined by curvilinear integral functionals and defining generalized monotonicity to measure the well-posedness, it is proven that the well-posedness is equivalent to the existence and uniqueness of solution. The mathematical development is accompanied by various illustrative examples.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2022)

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Article Mathematics, Applied

A consumption-investment model with state-dependent lower bound constraint on consumption

Chonghu Guan et al.

Summary: This paper investigates a life-time consumption-investment problem with a lower bound constraint on the consumption rate that depends linearly on the investor's wealth within the Black-Scholes framework. By transforming the problem into an equivalent stochastic control problem, an optimal consumption-investment strategy is provided, and the case of non-homogeneous constraint is discussed.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2022)

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Article Multidisciplinary Sciences

Numerical Investigation of Nonlinear Shock Wave Equations with Fractional Order in Propagating Disturbance

Jiahua Fang et al.

Summary: In this paper, a scheme using the Mohand transform and the homotopy perturbation method is developed to handle fractional-order shock wave equations and wave equations. The approach allows for obtaining series solutions from the recurrence relation after only a few iterations and presents approximate and precise solutions in the form of convergent results.

SYMMETRY-BASEL (2022)

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Article Economics

The market price of risk for delivery periods: Pricing swaps and options in electricity markets

Annika Kemper et al.

Summary: This paper introduces a market price for the delivery periods of electricity swaps in electricity markets and provides an arbitrage-free pricing framework for derivatives based on these contracts. The researchers use a weighted geometric averaging method to obtain the geometric swap price dynamics and consider typical features. The numerical study highlights the differences between different models depending on the delivery period.

ENERGY ECONOMICS (2022)

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Article Mathematics, Applied

Study of weak solutions of variational inequality systems with degenerate parabolic operators and quasilinear terms arising Americian option pricing problems

Jia Li et al.

Summary: This paper studies variational inequality systems with quasilinear degenerate parabolic operators in a bounded domain. The existence of weak solutions is proved by a limit process, and the uniqueness of the solution is also established.

AIMS MATHEMATICS (2022)

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Article Mathematics, Applied

Optimal variational iteration method for parametric boundary value problem

Qura Tul Ain et al.

Summary: The optimal variational iteration method (OVIM) is used to construct a fast and accurate algorithm for a special fourth-order ordinary initial value problem. A new method and a convergence control parameter are proposed to solve parametric boundary value problem that cannot be addressed by conventional methods. The advantages of different strategies for approximating the convergence control parameter are discussed.

AIMS MATHEMATICS (2022)

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Article Chemistry, Multidisciplinary

He-Laplace variational iteration method for solving the nonlinear equations arising in chemical kinetics and population dynamics

Muhammad Nadeem et al.

Summary: This article introduces an alternative method for studying partial differential equations, known as the He-Laplace variational iteration method. The method combines variational iteration method with Laplace transforms method, and employs He's polynomials obtained by the homotopy perturbation method to handle nonlinear terms. The accuracy and stability of this method are demonstrated on Fisher equation, generalized Fisher equation, and the nonlinear diffusion equation of the Fisher type.

JOURNAL OF MATHEMATICAL CHEMISTRY (2021)

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Article Mathematics, Applied

Analytically pricing volatility swaps and volatility options with discrete sampling: Nonlinear payoff volatility derivatives

Sanae Rujivan et al.

Summary: This paper introduces analytical pricing formulas for volatility swaps and volatility options, utilizing properties of noncentral chi random variables to compute expectations and obtain pricing formulas. The results are extended to the Black-Scholes model and Heston stochastic volatility model, demonstrating accuracy and efficiency compared to Monte Carlo simulations.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2021)

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Article Mathematics, Applied