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

Posted: 13 Feb 2001

See all articles by Cristian Ioan Tiu

Cristian Ioan Tiu

University at Buffalo; TIAA Institute


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.

Suggested Citation

Tiu, Cristian Ioan, On Level Curves of Value Functions in Optimization Models of Expected Utility. Available at SSRN: https://ssrn.com/abstract=242895

Cristian Ioan Tiu (Contact Author)

University at Buffalo ( email )

238 Jacobs Management Center
Jacobs Hall, North Campus
Buffalo, NY NY 14260
United States
7166453299 (Phone)

TIAA Institute ( email )

8500 Andrew Carnegie Blvd
Charlotte, NC 28262
United States

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