2014/09/11 by David Hobson, Hobson, David, Yeqi Zhu +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #91G10 #93E20 #Economic theories and models #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Portfolio Management (q-fin.PM) #Risk and Portfolio Optimization #Stochastic processes and financial applications #msc:91G10 #msc:93E20 #q-fin.MF #q-fin.PM
paper · pdf · doi:10.48550/arxiv.1409.3394
arxiv created 2014/09/11 · openalex publication_date 2014/09/11 · arxiv updated 2014/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we consider a special case of an optimal consumption/optimal portfolio problem first studied by Constantinides and Magill and by Davis and Norman, in which an agent with constant relative risk aversion seeks to maximise expected discounted utility of consumption over the infinite horizon, in a model comprising a risk-free asset and a risky asset with proportional transaction costs. The special case that we consider is that the cost of purchases of the risky asset is infinite, or equivalently the risky asset can only be sold and not bought. In this special setting new solution techniques are available, and we can make considerable progress towards an analytical solution. This means we are able to consider the comparative statics of the problem. There are some surprising conclusions, such as consumption rates are not monotone increasing in the return of the asset, nor are the certainty equivalent values of the risky positions monotone in the risk aversion.