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On Level Curves of Value Functions in Optimization Models of Expected Utility

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  • Cristian-Ioan Tiu
  • Thaleia Zariphopoulou
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    Abstract

    We study the level sets of value functions in expected utility stochastic optimization models. We consider optimal portfolio management models in complete markets with lognormally distributed prices as well as asset prices modeled as diffusion processes with nonlinear dynamics. Besides the complete market cases, we analyze models in markets with frictions like correlated nontraded assets and diffusion stochastic volatilities. We derive, for all the above models, equations that their level curves solve and we relate their evolution to power transformations of derivative prices. We also study models with proportional transaction costs in a finite horizon setting and we derive their level curve equation; the latter turns out to be a Variational Inequality with mixed gradient and obstacle constraints. Copyright Blackwell Publishers, Inc..

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 10 (2000)
    Issue (Month): 2 ()
    Pages: 323-338

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    Handle: RePEc:bla:mathfi:v:10:y:2000:i:2:p:323-338

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    Cited by:
    1. Bibiana Alarcon & Antonio Aguado & Resmundo Manga & Alejandro Josa, 2010. "A Value Function for Assessing Sustainability: Application to Industrial Buildings," Sustainability, MDPI, Open Access Journal, vol. 3(1), pages 35-50, December.

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