# Discrete time portfolio optimisation managing value at risk under heavy tail return distribution

## TL;DR

This paper develops a discrete-time portfolio optimization model that maximizes expected utility while managing Value at Risk under heavy-tailed return distributions, using Markov Decision Processes and numerical methods.

## Contribution

It introduces a novel approach combining Markov Decision Processes with both parametric and non-parametric heavy-tailed distributions for portfolio optimization under VaR constraints.

## Key findings

- Optimal strategies derived for heavy-tailed distributions.
- Numerical methods effectively handle non-parametric cases.
- Model enhances risk management in portfolio optimization.

## Abstract

We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to the Value at Risk assuming a heavy tail distribution of the stock prices return. We use Markov Decision Process and dynamic programming principle to get the optimal strategies and the value function which maximize the expected utility for parametric as well as non parametric distributions. Due to lack of explicit solution in the non parametric case, we use numerical integration for optimization