WELL-POSEDNESS OF PORTFOLIO CHOICE PROBLEMS WITH RISK MEASURES AND FRICTIONS
Alejandro Balbás, Beatriz Balbás, Raquel Balbás
This paper studies a portfolio choice problem such that the pricing rule may in-corporate transaction costs and the risk measure is coherent and expectation bounded. We will prove the necessity of dealing with pricing rules such that there exists an essentially bounded stochastic discount factor, which must be also bounded from below by a strictly positive value. Otherwise good deals will be available to traders, i.e., depending on the selected risk measure, investors can build portfolios whose (risk, return) will be as close as desired to (-infinity, infinity) or (0, infinity). This pathologic property still holds for vector risk measures (i.e., if we minimize a vector valued function whose components are risk measures). It is worthwhile to point out that essentially bounded stochastic discount factors are not usual in financial literature. In particular, the most famous frictionless, complete and arbitrage free pricing models imply the existence of good deals for every coherent and expectation bounded (scalar or vector) measure of risk, and the incorporation of transaction costs will not guarantee the solution of this caveat.
Lecture Notes in Management Science (2011) Vol. 3: 7-12
3rd International Conference on Applied Operational Research, Proceedings
© Tadbir Operational Research Group Ltd. All rights reserved.
ISSN 2008-0050 (Print)
ISSN 1927-0097 (Online)
· Extended Abstract