Dynamic exponential utility indifference valuation

• 成果类型: Article
• 署名作者: Mania, M; Schweizer, M
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000395
• 发表日期: 2005
• 页码: 2113-2143
• 关键词: Risk measures; maximization; DECOMPOSITION; prices

摘要

We study the dynamics of the exponential utility indifference value process C(B; alpha) for a contingent claim B in a semimartingale model with a general continuous filtration. We prove that C(B; alpha) 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 C-t (B; alpha). We obtain continuity in B and local Lipschitz-continuity in the risk aversion alpha, uniformly in t, and we extend earlier results on the asymptotic behavior as alpha SE arrow 0 or alpha NE arrow infinity to our general setting. Moreover, we also prove convergence of the corresponding hedging strategies.