Variational inequality arising from variable annuity with mean reversion environment

In this paper, we study a variational inequality arising from variable annuity (VA) to find the optimal surrender strategy for a VA investor when the underlying asset follows a mean reverting process. We formulate the problem as a free boundary partial differential equation (PDE) to obtain the optim...

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Bibliographic Details
Published in:Journal of inequalities and applications 2023-08, Vol.2023 (1), p.99-20, Article 99
Main Authors: Jeon, Junkee, Kim, Geonwoo
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Commodities
Currency
Free boundaries
Hedging
Inequality
Insurance premiums
Integral equations
Interest rates
Mathematical analysis
Mathematics
Mathematics and Statistics
Mean reversion
Mellin transforms
Optimal surrender boundary
Partial differential equations
Policyholders
Valuation
Variable annuities
Variable annuity
Variational inequality
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Summary:In this paper, we study a variational inequality arising from variable annuity (VA) to find the optimal surrender strategy for a VA investor when the underlying asset follows a mean reverting process. We formulate the problem as a free boundary partial differential equation (PDE) to obtain the optimal strategy. The PDE is solved analytically by the Mellin transform approach. Using the Mellin transform, we derive the integral equations for the value of the VA and the optimal surrender boundary. Since the solutions are obtained as the integral equations, we use the recursive integration method to determine the optimal surrender strategy. Finally, we provide the optimal surrender boundaries and values of VA with respect to some significant parameters to show the impacts of mean reversion.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-023-03015-y