# Comparison results for highly degenerate parabolic equations with univariate convex data and optimal strategies for options on trading accounts

## TL;DR

This paper establishes a comparison principle for highly degenerate parabolic equations with univariate convex data, and applies it to develop optimal trading strategies for symmetric passport options.

## Contribution

It introduces a comparison result for degenerate parabolic equations and applies it to derive strategies for a new financial product, symmetric passport options.

## Key findings

- Monotonicity of coefficients implies monotonicity of value functions.
- Comparison result applies to symmetric passport options.
- Provides a theoretical foundation for optimal trading strategies.

## Abstract

For linear multivariate purely second order highla degenerated parabolic equations with univariate convex data, monotonicity of the coefficent matrices implies monotonicity of the related value functions under usual regularity and growth assumptions for the data and the coefficients. The comparison result is applied to a new product, i.e., symmetric passport options.