2005/08/25 by Michael Mania, Martin Schweizer
Mathematics · Economics, Econometrics and Finance · #math.PR #q-fin.CP #msc:91B28 #msc:60H10 #msc:91B16 #msc:60G48
paper · pdf · doi:10.1214/105051605000000395
published as Annals of Applied Probability 2005, Vol. 15, No. 3, 2113-2143 · Published at http://dx.doi.org/10.1214/105051605000000395 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
arxiv created 2005/08/25 · arxiv updated 2009/12/01
We study the dynamics of the exponential utility indifference value process C(B;α) for a contingent claim B in a semimartingale model with a general continuous filtration. We prove that C(B;α) is (the first component of) the unique solution of a backward stochastic differential equation with a quadratic generator and obtain BMO estimates for the components of this solution. This allows us to prove several new results about Ct(B;α). We obtain continuity in B and local Lipschitz-continuity in the risk aversion α, uniformly in t, and we extend earlier results on the asymptotic behavior as α\searrow0 or α\nearrow∞ to our general setting. Moreover, we also prove convergence of the corresponding hedging strategies.