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Simple Bounds for Utility Maximization with Small Transaction Costs
TL;DR: In this paper, the approximation of the frictionless wealth process in markets with proportional transaction costs was studied and a lower bound for the frictional value function was derived for utilities with bounded risk aversion, paving the way for its asymptotic analysis using stability results for viscosity solutions.
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Abstract: Using elementary arguments, we show how to derive $\mathbf{L}_p$-error bounds for the approximation of frictionless wealth process in markets with proportional transaction costs. For utilities with bounded risk aversion, these estimates yield lower bounds for the frictional value function, which pave the way for its asymptotic analysis using stability results for viscosity solutions. Using tools from Malliavin calculus, we also derive simple sufficient conditions for the regularity of frictionless optimal trading strategies, the second main ingredient for the asymptotic analysis of small transaction costs.
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Jean Jacod,Albert N. Shiryaev +1 more
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TL;DR: In this article, the General Theory of Stochastic Processes, Semimartingales, and Stochastically Integrals is discussed and the convergence of Processes with Independent Increments is discussed.
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The Malliavin Calculus and Related Topics
David Nualart
- 09 May 1995
TL;DR: The Malliavin calculus as mentioned in this paper is an infinite-dimensional differential calculus on a Gaussian space, originally developed to provide a probabilistic proof to Hormander's "sum of squares" theorem, but it has found a wide range of applications in stochastic analysis.
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