Numerical performance of penalty method for American option pricing

Zhang, K.; Yang, Xiaoqi; Wang, Song; Teo, Kok Lay

doi:10.1080/10556780903051930

Cited by 14 publications

(10 citation statements)

References 12 publications

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“…It is worth noting that a monotonic convergence property for the solution sequence {x λm } w.r.t. the penalty parameter λ m is usually held when the power penalty method is used to approach to the one-side/unilateral obstacle problems, see [12,14,15,17], etc. However, for the double obstacle problems, due to the existence of two-side/bilateral obstacles, the monotonic convergence property is not held any longer.…”

Section: Theorem 32 Let X *mentioning

confidence: 99%

“…The above complementarity form inspires us to apply the power penalty method to solve Problem 1, since the method has been demonstrated to be a very successful means to solve general complementarity problems, see, for example [12,14,15,17]. The advantages of the power penalty method lie in several aspects.…”

mentioning

confidence: 99%

“…This implies that A is an M -matrix. It is also worth noting that the above assumption is normally guaranteed by a proper discretization method such as the upwind finite/difference/finite element or a fitted finite volume method for the differential equations in the continuous problem associated with Problem 1 (see, for example, [17]).…”

mentioning

confidence: 99%

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Solution method for discrete double obstacle problems based on a power penalty approach

Zhang¹,

Yang²,

Wang³

2022

JIMO

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<p style="text-indent:20px;">We develop a power penalty approach to a finite-dimensional double obstacle problem. This problem is first approximated by a system of nonlinear equations containing two penalty terms. We show that the solution to this penalized equation converges to that of the original obstacle problem at an exponential rate when the coefficient matrices are <inline-formula><tex-math id="M1">\begin{document}$ M $\end{document}</tex-math></inline-formula>-matrices. Numerical examples are presented to confirm the theoretical findings and illustrate the efficiency and effectiveness of the new method.</p>

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Section: Theorem 32 Let X *mentioning

confidence: 99%

mentioning

confidence: 99%

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Solution method for discrete double obstacle problems based on a power penalty approach

Zhang¹,

Yang²,

Wang³

2022

JIMO

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“…Remark 2.2. It is worth noting that the above assumption is normally guaranteed by a proper discretization method such as the upwind finite difference/finite element or a fitted finite volume method for 2nd order elliptic partial differential equations (see, for example, [13]).…”

Section: Penalty Approachmentioning

confidence: 99%

A power penalty method for discrete HJB equations

Zhang

Yang

2020

Optim Lett

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We develop a power penalty approach to the discrete Hamilton-Jacobi-Bellman (HJB) equation in R N in which the HJB equation is approximated by a nonlinear equation containing a power penalty term. We prove that the solution to this penalized equation converges to that of the HJB equation at an exponential rate with respect to the penalty parameter when the control set is finite and the coefficient matrices are M -matrices. Examples are presented to confirm the theoretical findings and to show the efficiency of the new method.

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“…As such, optimization and control of the stochastic dynamical system are a challenging topic. In the past decades, the research outcomes, both for theoretical results and development of the algorithms, are well-defined [9] [10] [11] [12] [13]. In general, the real processes, which are modeled into the stochastic optimal control problem, are mostly nonlinear process.…”

Section: Introductionmentioning

confidence: 99%

Least Squares Solution for Discrete Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

Kek¹,

Li²,

Teo³

2017

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In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.

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Numerical performance of penalty method for American option pricing

Cited by 14 publications

References 12 publications

Solution method for discrete double obstacle problems based on a power penalty approach

Solution method for discrete double obstacle problems based on a power penalty approach

A power penalty method for discrete HJB equations

Least Squares Solution for Discrete Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

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