Abstract
A discrete-time financial market model is considered with a sequence of investors whose preferences are described by concave strictly increasing functions defined on the positive axis. Under suitable conditions, we show that the utility indifference prices of a bounded contingent claim converge to its superreplication price when the investors’ absolute risk-aversion tends to infinity.
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References
Arrow K (1965) Essays in the theory of risk-bearing. North-Holland, Amsterdam
Bouchard B (2000) Stochastic control and applications in finance. PhD thesis, Université Paris 9
Bouchard B, Kabanov YuM, Touzi N (2001) Option pricing by large risk aversion utility under transaction costs. Decis Econ Finance 24:127–136
Carassus L, Rásonyi M (2006a) Optimal strategies and utility-based prices converge when agents’ preferences do. Forthcoming in Math Oper Res
Carassus L, Rásonyi M (2006b) Convergence of utility indifference prices to the superreplication price: the whole real line case (submitted)
Cheridito P, Summer Ch (2006) Utility-maximizing strategies under incresing risk aversion in one-period models. Finance Stoch 10:147–158
Collin-Dufresne P, Hugonnier J (2004) Pricing and hedging in the presence of extraneous risks (working paper)
Cvitanić J, Karatzas I (1993) Hedging contingent claims with constrained portfolios. Ann Appl Probab 3:652–681
Delbaen F, Grandits P, Rheinländer T, Samperi D, Schweizer M, Stricker Ch (2002) Exponential hedging and entropic penalties. Math Finance 12:99–123
El Karoui N, Quenez MC (1995) Dynamic programming and pricing of contingent claims in an incomplete market. SIAM J Control Optim 33:29–66
Föllmer H, Kabanov YuM (1998) Optional decomposition and Lagrange multipliers. Finance Stoch 2:69–81
Hodges R, Neuberger K (1989) Optimal replication of contingent claims under transaction costs Rev Futures Mkts 8:222–239
Jacod J, Shiryaev AN (1998) Local martingales and the fundamental asset pricing theorems in the discrete-time case. Finance Stoch 2:259–273
Jouini E, Kallal H (2001) Efficient trading strategies in the presence of market frictions. Rev Financ Stud 14:343–369
Kabanov YuM, Stricker Ch (2001) A teachers’ note on no-arbitrage criteria. Sémin Probab 37:149–152. Springer, Berlin Heidelberg New York
Korn R, Schäl M (1999) On value preserving and growth optimal portfolios. Math Methods Oper Res 50:189–218
Kramkov DO (1996) Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets. Probab Theory Relat Fields 105:459–479
Pratt J (1964) Risk aversion in the small and in the large. Econometrica 32:122–136
Rásonyi M, Stettner L (2005) On the utility maximization problem in discrete-time financial market models. Ann Appl Probab 15:1367–1395
Rásonyi M, Stettner L (2006) On the existence of optimal portfolios for the utility maximization problem in discrete time financial market models. In: Kabanov Yu, Liptser R, Stoyanov J (ed) From stochastic calculus to mathematical finance, The Shiryaer Festschrift, pp 589–608
Rouge R, El Karoui N (2000): Pricing via utility maximization and entropy. Math Finance 10:259–276
Schäl M (2000) Portfolio optimization and martingale measures. Math Finance 10:289–303
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Carassus, L., Rásonyi, M. Convergence of Utility Indifference Prices to the Superreplication Price. Math Meth Oper Res 64, 145–154 (2006). https://doi.org/10.1007/s00186-006-0074-4
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DOI: https://doi.org/10.1007/s00186-006-0074-4