Risk averse asymptotics and the optional decomposition
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 2, pp. 409-418 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem of maximizing expected utility for a general utility function on $\textbf R$ when the agent becomes increasingly risk averse. The limiting strategy will be shown to be a special, unique superhedging strategy, the so-called balanced strategy. The connections to the optional decomposition and the class of minimal hedging strategies described in [D. O. Kramkov, Probab. Theory Related Fields, 105 (1996), pp. 459–479] are examined.
Keywords: hedging, exponential utility, risk aversion
Mots-clés : optional decomposition.
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P. Grandits; Ch. Summer. Risk averse asymptotics and the optional decomposition. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 2, pp. 409-418. http://geodesic.mathdoc.fr/item/TVP_2006_51_2_a11/

[1] Arrow K. J., Essays in the Theory of Risk-bearing, North-Holland, Amsterdam, 1970 | MR | Zbl

[2] Cheridito P., Summer C., “Utility maximization under increasing risk aversion in one-period models”, Finance Stoch., 10 (2006), 147–158 | DOI | MR

[3] Delbaen F., Grandits P., Rheinländer T., Samperi D., Schweizer C., Stricker C., “Exponential hedging and entropic penalties”, Math. Finance, 12:2 (2002), 99–123 | DOI | MR | Zbl

[4] Harrison J. M., Pliska S. R., “Martingales and stochastic integrals in the theory of continuous trading”, Stochastic Process. Appl., 11:3 (1981), 215–260 | DOI | MR | Zbl

[5] Kramkov D. O., “Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets”, Probab. Theory Related Fields, 105:4 (1996), 459–479 | MR | Zbl

[6] Pratt J., “Risk aversion in the small and in the large”, Econometrica, 32 (1964), 122–136 | DOI | Zbl

[7] Rokafellar R., Vypuklyi analiz, Mir, M., 1973, 469 pp.

[8] Schweizer M., “Variance-optimal hedging in discrete time”, Math. Oper. Res., 20:1 (1995), 1–32 | DOI | MR | Zbl

[9] Summer C., Utility maximization and increasing risk aversion, Ph. D. Thesis, Vienna University of Technology, Vienna, 2002