Homogenization and Asymptotics for Small Transaction Costs

Halil Mete Soner and Nizar Touzi
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Halil Mete Soner: ETH Zürich, Ecole Polytechnique Fédérale de Lausanne, and Swiss Finance Institute
Nizar Touzi: Ecole Polytechnique, Paris

No 12-13, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic control problem which can be solved in closed form in the one-dimensional case. Unlike the existing literature, we consider a general utility function and general dynamics for the underlying assets. Our arguments are based on ideas from the homogenization theory and use the convergence tools from the theory of viscosity solutions. The multidimensional case is studied in our accompanying paper using the same approach.

Keywords: transaction costs; homogenization; viscosity solutions; asymptotic expansions (search for similar items in EconPapers)
JEL-codes: D40 G11 G12 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2012-03
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1213

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