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On Level Curves of Value Functions in Optimization Models of Expected Utility
Author(s) -
Tiu CristianIoan,
Zariphopoulou Thaleia
Publication year - 2000
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00097
Subject(s) - portfolio optimization , economics , incomplete markets , transaction cost , portfolio , econometrics , mathematical optimization , mathematics , mathematical economics , financial economics , microeconomics
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.