Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/258503 
Year of Publication: 
2021
Citation: 
[Journal:] Journal of Risk and Financial Management [ISSN:] 1911-8074 [Volume:] 14 [Issue:] 9 [Article No.:] 399 [Publisher:] MDPI [Place:] Basel [Year:] 2021 [Pages:] 1-12
Publisher: 
MDPI, Basel
Abstract: 
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.
Subjects: 
finite difference approximation
Hamilton-Jacobi-Bellman equation
option pricing
penalty methods
transaction costs
utility indifference pricing
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article

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