Summary: Decisions in Economics and Finance manuscript No.
(will be inserted by the editor)
Shortfall Risk Minimization in a Discrete Regime Switching Model
Northern Illinois University, Department of Mathematical Sciences, Dekalb, IL, 60115
The date of receipt and acceptance will be inserted by the editor
Mathematics Subject Classification (2000): 49L20, 90C39, 91B28, 91B70, 93C55
Journal of Economic Literature Classification Number : D81, G11, G13
There have been profound ideas on how to measure risk which have influenced the financial market.
Shortfall risk minimization is one of these methods which has attracted considerable attention. This
problem has been studied for the binomial model in Runggaldier et al (2000) and Runggaldier et al
(2002) and for the trinomial model in Scagnelatto and Vargiolu (2002). In this paper, we investigate
the shortfall risk minimization in a discrete regime switching model. In the model, we have two
possible regimes, which are both binomial. To fix the ideas, we can think of the second regime
as being the consequence of the presence of inside information, but this can also be due to other
factors. Explicit solutions for one-period models are given.
The binomial model has as limiting case the Black-Scholes model, c.f. Musiela and Rutkowski
(1997), while the trinomial model has limiting case a stochastic volatility model, c.f. Avallaneda
et al (1995). The discrete model used in this paper was introduced in Guo (1999) and was shown