Financial Engineering Seminar
February, 23, 2005(Wed)
1:55 PM - 2:45 PM (7th period),
Weil Hall 303 (conference room)
Incomplete markets: non uniqueness and convergence
Phelim P Boyle,
School of Accountancy
University of Waterloo
Abstract:
This paper deals with two aspects of market incompleteness. The first is the
non uniqueness of the market price of risk. When markets are incomplete,
the absence of arbitrage implies that there will be a multiplicity of equivalent
martingale measures. Equivalently the absence of arbitrage is not enough to
specify the stochastic discount factor. The second is related to the notion of
robustness when there is model error. We propose a unified framework for
analyzing both these aspects of incomplete markets. Our approach provides a
convenient framework for addressing model mis specification error, distance
between an incomplete model and a benchmark complete model, and the
mis-estimation of the market price of risk. We outline the approach using
stochastic volatility models and illustrate it with examples. This talk is based
on joint work with Shui Feng of McMaster University and Weidong Tian of
the University of Waterloo.