A high-order deferred correction method for the solution of free boundary problems using penalty iteration, with an application to American option pricing

Wang, Dawei; Serkh, Kirill; Christara, Christina C.

doi:10.1016/j.cam.2023.115272

Journal of Computational and Applied Mathematics

2023

DOI: 10.1016/j.cam.2023.115272

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A high-order deferred correction method for the solution of free boundary problems using penalty iteration, with an application to American option pricing

Dawei Wang

Kirill Serkh

Christina C. Christara

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Local Hölder continuity of nonnegative weak solutions of inverse variation-inequality problems of non-divergence type

Dong

2024

era

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<abstract><p>Compared to the standard variational inequalities, inverse variational inequalities are more suitable for pricing American options with indefinite payoff. This paper investigated the initial-boundary value problem of inverse variational inequalities constituted by a class of non-divergence type parabolic operators. We established the existence and Hölder continuity of weak solutions. Since the comparison principle in the case of standard variational inequalities is no longer applicable, we constructed an integral inequality using differential inequalities to determine the global upper bound of the solution. By combining it with the continuous method, we obtained the existence of weak solutions. Additionally, by employing truncation factors, we obtained the lower bound of weak solutions in the cylindrical subdomain, thereby obtaining the Hölder continuity.</p></abstract>

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Local Hölder continuity of nonnegative weak solutions of inverse variation-inequality problems of non-divergence type

Dong

2024

era

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Local Hölder continuity of inverse variation-inequality problem constructed by non-Newtonian polytropic operators in finance

Li,

Tong

2023

MATH

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A high-order deferred correction method for the solution of free boundary problems using penalty iteration, with an application to American option pricing

Cited by 2 publications

References 24 publications

Local Hölder continuity of nonnegative weak solutions of inverse variation-inequality problems of non-divergence type

Local Hölder continuity of nonnegative weak solutions of inverse variation-inequality problems of non-divergence type

Local Hölder continuity of inverse variation-inequality problem constructed by non-Newtonian polytropic operators in finance

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