Convex duality for stochastic differential utility
This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and stochastic differential utility. For Epstein-Zin utility, duality between the primal and dual problems is established. Consequently the optimal strategy of the consumption and investment problem is identified without assuming several technical conditions on market model, utility specification, and agent's admissible strategy. Meanwhile the minimizer of the dual problem is identified as the utility gradient of the primal value and is economically interpreted as the "least favorable" completion of the market.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Deep Learning for Constrained Utility Maximisation
This paper proposes two algorithms for solving stochastic control problems with deep learning, with a focus on the utility maximisation problem. The first algorithm solves Markovian problems via the Hamilton Jacobi Bellm…
Deep LearningOptimal 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 …
Utility 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…
Efficient Privacy-Preserving Stochastic Nonconvex Optimization
While many solutions for privacy-preserving convex empirical risk minimization (ERM) have been developed, privacy-preserving nonconvex ERM remains a challenge. We study nonconvex ERM, which takes the form of minimizing a…
Privacy PreservingMirror Descent Algorithms with Nearly Dimension-Independent Rates for Differentially-Private Stochastic Saddle-Point Problems
We study the problem of differentially-private (DP) stochastic (convex-concave) saddle-points in the polyhedral setting. We propose $(\varepsilon, \delta)$-DP algorithms based on stochastic mirror descent that attain nea…
LEMMA