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Exponential utility maximization and indifference valuation with unbounded payoffs

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  • Ying Hu
  • Gechun Liang
  • Shanjian Tang

Abstract

We solve an exponential utility maximization problem with unbounded payoffs and portfolio constraints, via the theory of quadratic backward stochastic differential equations with unbounded terminal data. This generalizes the previous work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] from the bounded to an unbounded framework. Furthermore, we study utility indifference valuation of financial derivatives with unbounded payoffs, and derive a novel convex dual representation of the prices. In particular, we obtain new asymptotic behavior as the risk aversion parameter tends to either zero or infinity.

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  • Ying Hu & Gechun Liang & Shanjian Tang, 2017. "Exponential utility maximization and indifference valuation with unbounded payoffs," Papers 1707.00199, arXiv.org, revised Jul 2018.
    • Handle: RePEc:arx:papers:1707.00199
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    References listed on IDEAS

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    1. Vicky Henderson & Gechun Liang, 2014. "Pseudo linear pricing rule for utility indifference valuation," Finance and Stochastics, Springer, vol. 18(3), pages 593-615, July.
    2. Freddy Delbaen & Peter Grandits & Thorsten Rheinländer & Dominick Samperi & Martin Schweizer & Christophe Stricker, 2002. "Exponential Hedging and Entropic Penalties," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 99-123, April.
    3. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
    4. Becherer, Dirk, 2003. "Rational hedging and valuation of integrated risks under constant absolute risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 1-28, August.
    5. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    6. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Papers math/0508489, arXiv.org.
    7. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276, April.
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    Cited by:

    1. Wing Fung Chong & Ying Hu & Gechun Liang & Thaleia Zariphopoulou, 2019. "An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior," Finance and Stochastics, Springer, vol. 23(1), pages 239-273, January.
    2. Ying Hu & Gechun Liang & Shanjian Tang, 2018. "Systems of ergodic BSDEs arising in regime switching forward performance processes," Papers 1807.01816, arXiv.org, revised Jun 2020.
    3. Matthew O. Adaji, 2023. "Mathematical Model for the Determination of Optimal Salary in Defined Benefit Pension Plan with Early Retirement, An Application of Smooth-Pasting Condition," International Journal of Research and Innovation in Applied Science, International Journal of Research and Innovation in Applied Science (IJRIAS), vol. 8(9), pages 128-144, September.
    4. Dingqian Sun, 2020. "The convergence rate from discrete to continuous optimal investment stopping problem," Papers 2004.14627, arXiv.org.

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