SINGULAR PERTURBATION EXPANSION for UTILITY MAXIMIZATION with ORDER-∈ QUADRATIC TRANSACTION COSTS

Shiva Chandra; Andrew Papanicolaou

doi:10.1142/S0219024919500390

SINGULAR PERTURBATION EXPANSION for UTILITY MAXIMIZATION with ORDER-∈ QUADRATIC TRANSACTION COSTS

Shiva Chandra, Andrew Papanicolaou

Finance and Risk Engineering

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

Abstract

We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman equation whose solution can be expanded in powers of √∈. In this paper, we derive explicit formulae for the first two terms of this expansion. Analysis and simulation are provided to show the behavior of this approximating solution.

Original language	English (US)
Article number	1950039
Journal	International Journal of Theoretical and Applied Finance
Volume	22
Issue number	7
DOIs	https://doi.org/10.1142/S0219024919500390
State	Published - Nov 1 2019

Keywords

Merton problem
Transaction costs
aim portfolio
singular perturbation expansion
stochastic control

ASJC Scopus subject areas

General Economics, Econometrics and Finance
Finance

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10.1142/S0219024919500390

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KW - singular perturbation expansion

KW - stochastic control

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SINGULAR PERTURBATION EXPANSION for UTILITY MAXIMIZATION with ORDER-∈ QUADRATIC TRANSACTION COSTS

Abstract

Keywords

ASJC Scopus subject areas

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