# Monotone 2D Integration Scheme for Mean-CVaR Optimization via Fourier-Trained Transition Kernels

arXiv: https://arxiv.org/abs/2603.26291 · HTML: https://mlsanity.com/paper/2603.26291/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2026.

## Built on by (most cited first, 1 of 1)

- [A data-driven Fourier-mixture neural-network method for density estimation](https://mlsanity.com/paper/2605.18019/) (2026)

## Abstract (arXiv)

We present a strictly monotone, provably convergent two-dimensional (2D) integration method for multi-period mean-conditional value-at-risk (mean-CVaR) reward-risk stochastic control in models whose one-step increment law is specified via a closed-form characteristic function (CF). When the transition density is unavailable in closed form, we learn a nonnegative, normalized 2D transition kernel in Fourier space using a simplex-constrained Gaussian-mixture parameterization, and discretize the resulting convolution integrals with composite quadrature rules with nonnegative weights to guarantee monotonicity. The scheme is implemented efficiently using 2D fast Fourier transforms. Under mild Fourier-tail decay assumptions on the CF, we derive Fourier-domain L2 kernel-approximation and truncation error estimates and translate them into real-space bounds that are used to establish ℓ_∞-stability, consistency, and pointwise convergence as the discretization and kernel-approximation parameters vanish. Numerical experiments for a fully coupled 2D jump--diffusion model in a multi-period portfolio optimization setting illustrate robustness and accuracy.