Theoretical Statistics and Mathematics Unit, ISI Delhi

January 14, 2015 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Amogh Deshpande,
University of Liverpool, UK

Title:
On the role of Follmer-Schweizer minimal martingale measure in risk sensitive control asset management.

Abstract of Talk

Kuroda and Nagai state that the factor process in the Risk Sensitive control
Asset Management (RSCAM) is stable under the F¨ollmer-Schweizer minimal
martingale measure . Fleming and Sheu and more recently F¨ollmer and
Schweizer have observed that the role of the minimal martingale measure
in this portfolio optimization is yet to be established. In this talk we aim
to address this question by explicitly connecting the optimal wealth allocation
to the minimal martingale measure. We achieve this by using a “trick” of
observing this problem in the context of model uncertainty via a two person
zero sum stochastic diﬀerential game between the investor and an antagonistic
market that provides a probability measure. We obtain some startling insights.
Firstly, if short-selling is not permitted and if the factor process evolves under
the minimal martingale measure then the investor’s optimal strategy can only
be to invest in the riskless asset (i.e. the no-regret strategy). Secondly, if the
factor process and the stock price process have independent noise, then even if
the market allows short selling, the optimal strategy for the investor must be
the no-regret strategy while the factor process will evolve under the minimal
martingale measure.