Essays on consumption portfolio optimization with recursive utility in multi-asset markets
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This paper studies an optimal consumption–portfolio problem for an agent with the recursive utility. Chapter 1 focuses on the setting of large numbers of factors and assets. We first characterize optimal consumption-portfolio strategies by forward-backward stochastic differential equations. We propose a new approach based on deep neural networks (DNN), which allows us to solve optimal strategies in a financial market that is comprised of multiple assets efficiently. The accuracy of the new approach is tested by comparing it to the analytical solution when a closed-form solution is available. The efficiency is tested by solving a large-scale problem consisting of dozens of assets. In Chapter 2, we impose a trading constraint on the total position of the portfolio and prove that the DNN based method can also converge to the optimal solution with trading constraints. Based on these results, we provide concrete results about consumption-portfolio plans when trading constraints exist.