An Asymptotic Method to a Financial Optimization Problem

Dejun Xie; David Edwards; Giberto Schleiniger

doi:10.1007/978-90-481-3177-8_6

An Asymptotic Method to a Financial Optimization Problem

Dejun Xie^*, David Edwards, Giberto Schleiniger

^*Corresponding author for this work

University of Delaware

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

This paper studies the borrower's optimal strategy to close the mortgage when the volatility of the market investment return is small. Integral equation representation of the mortgage contract value is derived, then used to find the numerical solution of the free boundary. The asymptotic expansions of the free boundary are derived for both small time and large time. Based on these asymptotic expansions two simple analytical approximation formulas are proposed. Numerical experiments show that the approximation formulas are accurate enough from practitioner's point of view.

Original language	English
Pages (from-to)	79-94
Number of pages	16
Journal	Lecture Notes in Electrical Engineering
DOIs	https://doi.org/10.1007/978-90-481-3177-8_6
Publication status	Published - 2009
Externally published	Yes
Event	International Conference on Advances in Machine Learning and Data Analysis - Berkeley, CA, United States Duration: 22 Oct 2008 → 24 Oct 2008

Keywords

Analytical approximation
Asymptotic analysis
Mortgage prepayment
Numerical solution

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10.1007/978-90-481-3177-8_6

Cite this

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abstract = "This paper studies the borrower's optimal strategy to close the mortgage when the volatility of the market investment return is small. Integral equation representation of the mortgage contract value is derived, then used to find the numerical solution of the free boundary. The asymptotic expansions of the free boundary are derived for both small time and large time. Based on these asymptotic expansions two simple analytical approximation formulas are proposed. Numerical experiments show that the approximation formulas are accurate enough from practitioner's point of view.",

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AU - Edwards, David

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AB - This paper studies the borrower's optimal strategy to close the mortgage when the volatility of the market investment return is small. Integral equation representation of the mortgage contract value is derived, then used to find the numerical solution of the free boundary. The asymptotic expansions of the free boundary are derived for both small time and large time. Based on these asymptotic expansions two simple analytical approximation formulas are proposed. Numerical experiments show that the approximation formulas are accurate enough from practitioner's point of view.

KW - Analytical approximation

KW - Asymptotic analysis

KW - Mortgage prepayment

KW - Numerical solution

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ER -

An Asymptotic Method to a Financial Optimization Problem

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Keywords

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