Erschienen:
Institute of Mathematical Statistics, 2014
Erschienen in:
The Annals of Applied Probability, 24 (2014) 4, Seite 1554-1584
Sprache:
Englisch
DOI:
10.1214/13-AAP956
ISSN:
1050-5164
Entstehung:
Anmerkungen:
Beschreibung:
We consider a pair (X, Y) of stochastic processes satisfying the equation dX = a(X)Y dB driven by a Brownian motion and study the monotonicity and continuity in y of the value function v(x, y) = supτ Ex,y [e⁻qτ g(Xτ)], where the supremum is taken over stopping times with respect to the filtration generated by (X, Y). Our results can successfully be applied to pricing American options where X is the discounted price of an asset while Y is given by a stochastic volatility model such as those proposed by Heston or Hull and White. The main method of proof is based on time-change and coupling.