On the Uniqueness of Unbounded Viscosity Solutions Arising in an Optimal Terminal Wealth Problem with Transaction Costs
SIAM Journal on Control and Optimization, Vol. 53, No. 5, pp. 2878-2897, 2015.
Posted: 23 Aug 2013 Last revised: 3 May 2016
Date Written: March 5, 2015
We study the uniqueness of viscosity solutions of a Hamilton-Jacobi-Bellman equation which arises in a portfolio optimization problem in which an investor maximizes expected utility of terminal wealth in the presence of proportional transaction costs. Our main contribution is that the comparison theorem can be applied to prove the uniqueness of the value function in the portfolio optimization problem for logarithmic and power utility.
Keywords: unbounded viscosity solutions, comparison principle, optimal terminal wealth, transaction costs
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