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

Marcellino Gaudenzi and Michel Vellekoop

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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.

New Economics Papers: this item is included in nep-upt
Date: 2018-09
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