Asymptotic Theory of Transaction Costs

A classical topic in mathematical finance is the theory of portfolio optimization. Robert Merton's work from the early seventies had enormous impact on academic research, as well as on the paradigms guiding practitioners. One of the ramifications of this topic is the analysis of (small) proportional transaction costs, such as a Tobin tax. These lecture notes present some striking recent results of the asymptotic dependence of the relevant quantities when transaction costs tend to zero.