# Continuity of Utility Maximization under Weak Convergence

arXiv: https://arxiv.org/abs/1811.01420 · HTML: https://mlsanity.com/paper/1811.01420/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2018.

## Built on by (most cited first, 2 of 2)

- [Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controls](https://mlsanity.com/paper/2104.09311/) (2021)
- [Kernel Mean Embedding Topology: Weak and Strong Forms for Stochastic Kernels and Implications for Model Learning](https://mlsanity.com/paper/2502.13486/) (2025)

## Abstract (arXiv)

In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak convergence result for the terminal wealths of the optimal portfolios. Finally, we apply our results to the computation of the minimal expected shortfall (shortfall risk) in the Heston model by building an appropriate lattice approximation.