Dynamic Convex Duality in Constrained Utility Maximization
In this paper, we study a constrained utility maximization problem following the convex duality approach. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual problems in terms of FBSDEs plus additional conditions. Such formulation then allows us to explicitly characterize the primal optimal control as a function of the adjoint process coming from the dual FBSDEs in a dynamic fashion and vice versa. Moreover, we also find that the optimal primal wealth process coincides with the adjoint process of the dual problem and vice versa. Finally we solve three constrained utility maximization problems, which contrasts the simplicity of the duality approach we propose and the technical complexity of solving the primal problems directly.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Optimal portfolio under ratio-type periodic evaluation in stochastic factor models under convex trading constraints
This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on …
Portfolio Optimization under Shortfall Risk Constraint
This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of…
Portfolio OptimizationUtility maximization with addictive consumption habit formation in incomplete semimartingale markets
This paper studies the continuous time utility maximization problem on consumption with addictive habit formation in incomplete semimartingale markets. Introducing the set of auxiliary state processes and the modified du…
Utility maximization in pure-jump models driven by marked point processes and nonlinear wealth dynamics
We explore martingale and convex duality techniques to study optimal investment strategies that maximize expected risk-averse utility from consumption and terminal wealth. We consider a market model with jumps driven by …
Point ProcessesDual Iterative Hard Thresholding: From Non-convex Sparse Minimization to Non-smooth Concave Maximization
Iterative Hard Thresholding (IHT) is a class of projected gradient descent methods for optimizing sparsity-constrained minimization models, with the best known efficiency and scalability in practice. As far as we know, t…
Computational EfficiencyStochastic Optimization