Homogenization and Asymptotics for Small Transaction Costs
Halil Mete Soner
ETH Zürich; Swiss Finance Institute
Ecole Polytechnique, Paris
March 23, 2012
Swiss Finance Institute Research Paper No. 12-13
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.
Number of Pages in PDF File: 31
Keywords: transaction costs, homogenization, viscosity solutions, asymptotic expansions
JEL Classification: D40, G11, G12working papers series
Date posted: April 2, 2012
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