Abstract
We derive a martingale representation for a contingent claim
under a Markov-modulated version of the Black-Scholes economy. The martingale representation for the price of the claim is established with respect to
an equivalent martingale measure chosen by the Esscher transform. Under
some differentiability conditions for the coefficients of the price processes, we
shall identify explicitly the integrands in the martingale representation using stochastic flows. We shall introduce a zero-coupon bond to minimize the
residual risk due to incomplete hedging.
under a Markov-modulated version of the Black-Scholes economy. The martingale representation for the price of the claim is established with respect to
an equivalent martingale measure chosen by the Esscher transform. Under
some differentiability conditions for the coefficients of the price processes, we
shall identify explicitly the integrands in the martingale representation using stochastic flows. We shall introduce a zero-coupon bond to minimize the
residual risk due to incomplete hedging.
| Original language | English |
|---|---|
| Pages (from-to) | 279-292 |
| Journal | Communications on Stochastic Analysis |
| Volume | 1 |
| Issue number | 2 |
| Publication status | Published - 2007 |
| Externally published | Yes |