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Exact Solutions for Optimal Investment Strategies and Indifference Prices under Non-Differentiable Preferences

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  • Marcellino Gaudenzi
  • Michel Vellekoop

Abstract

We propose an algorithm to calculate the exact solution for utility optimization problems on finite state spaces under a class of non-differentiable preferences. We prove that optimal strategies must lie on a discrete grid in the plane, and this allows us to reduce the dimension of the problem and define a very efficient method to obtain those strategies. We also show how fast approximations for the value function can be obtained with an a priori specified error bound and we use these to replicate results for investment problems with a known closed-form solution. These results show the efficiency of our approach, which can then be used to obtain numerical solutions for problems for which no explicit formulas are known.

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  • Marcellino Gaudenzi & Michel Vellekoop, 2018. "Exact Solutions for Optimal Investment Strategies and Indifference Prices under Non-Differentiable Preferences," Papers 1809.11010, arXiv.org.
    • Handle: RePEc:arx:papers:1809.11010
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    References listed on IDEAS

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