Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs

Lesmana, Donny Citra; Wang, Song

doi:10.1016/j.amc.2014.11.060

Cited by 10 publications

(9 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Next, introduce the specific implementation of the penalty method for our pricing model following Wang (2009, 2014). The penalty method has been successfully adopted for solving various nonlinear option pricing model by Lesmana and Wang (2015), or Chernogorova et al (2018), and others. The optimal time dependent penalty function has been proposed recently by Clevenhaus et al (2020).…”

Section: Penalty Methods For Solving Hjb Equationsmentioning

confidence: 99%

Utility Indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation

Pólvora

Ševčovič

2021

JRFM

View full text Add to dashboard Cite

Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style of an option price is constructed as a difference of the certainty equivalents to the value functions solving the system of HJB equations. We introduce the transformation method for solving the penalized nonlinear partial differential equation. The transformed equation involves possibly non-constant the risk aversion function containing the negative ratio between the second and first derivatives of the utility function. Using comparison principles we derive useful bounds on the option price. We also propose a finite difference numerical discretization scheme with some computational examples.

show abstract

Section: Penalty Methods For Solving Hjb Equationsmentioning

confidence: 99%

Utility Indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation

Pólvora

Ševčovič

2021

JRFM

View full text Add to dashboard Cite

show abstract

“…We comment that, in practice, Assumption A1 is usually satisfied by a discretized system if an appropriate discretization scheme is used, as we have exampled in [23] using an NCP arising from the discretization of a nonlinear Black-Scholes equation. Using the above assumptions we are able to show the following lemma.…”

Section: The Interior Penalty Methodsmentioning

confidence: 99%

“…Recently, penalty methods have been used extensively for solving both finite-and finite-dimensional NCPs arising in classic and financial engineering [2,17,28,37,18,35,19,20,43,33,26,5,23,34]. More specifically, a power penalty method is proposed for Problem 1.2 in [36] in which a penalty term is used to penalize the infeasible components of an approximation to the relaxed unconstrained problem.…”

Section: Introductionmentioning

confidence: 99%

An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem

Wang

2018

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

We propose and analyze an interior penalty method for a finite-dimensional large-scale bounded Nonlinear Complementarity Problem (NCP) arising from the discretization of a differential double obstacle problem in engineering. Our approach is to approximate the bounded NCP by a nonlinear algebraic equation containing a penalty function with a penalty parameter µ > 0. The penalty equation is shown to be uniquely solvable. We also prove that the solution to the penalty equation converges to the exact one at the rate O(µ 1/2) as µ → 0. A smooth Newton method is proposed for solving the penalty equation and it is shown that the linearized system is reducible to two decoupled subsystems. Numerical experiments, performed on some nontrivial test examples, demonstrate the computed rate of convergence matches the theoretical one.

show abstract

“…As mentioned before, A(p) in 3is usually a positive-definite symmetric matrix if an appropriate numerical scheme such as one of those in [22,42,27,23] is used for the discretization of (1). Thus, there exists a positive constant α such that…”

Section: Preliminariesmentioning

confidence: 99%

Numerical solution of an obstacle problem with interval coefficients

Wang¹

2020

Numerical Algebra, Control &Amp; Optimization

Self Cite

View full text Add to dashboard Cite

In this work we propose a novel numerical method for a finitedimensional optimization problem arising from the discretization of an infinitedimensional constrained optimization problem, called an obstacle problem, with interval coefficients. In this method, the two different ways of characterizing the optimal solutions, i.e., minimizing the mid-point and one end-point (the worst-case scenario) or the mid-point and the width of the objective interval, are formulated as a single constrained multi-objective minimization problem and the KKT conditions of the optimization problem defining the Pareto optimal solution to the multi-objective problem are of the form of a Linear Complementarity Problem (LCP) which is shown to have a unique solution. The LCP is the approximated by a non-linear equation using an interior penalty approach. We prove that the penalty equation is uniquely solvable and its solution converges to that of LCP as the penalty constant approaches to zero. Numerical results are presented to demonstrate the usefulness of the numerical method proposed.

show abstract

Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs

Cited by 10 publications

References 24 publications

Utility Indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation

Utility Indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation

An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem

Numerical solution of an obstacle problem with interval coefficients

Contact Info

Product

Resources

About