# Portfolio Optimization Managing Value at Risk under Heavy Tail Return, using Stochastic Maximum Principle

## TL;DR

This paper develops a stochastic maximum principle-based approach for portfolio optimization under heavy-tailed return distributions, focusing on managing Value at Risk without assuming specific distribution forms, and demonstrates its effectiveness with real data.

## Contribution

It introduces a non-parametric calibration method for portfolio optimization under heavy tails using stochastic maximum principle, with empirical validation.

## Key findings

- Close alignment with financial intuition
- Effective handling of heavy-tailed distributions
- Practical applicability demonstrated with real data

## 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 managing the Value at Risk (VaR) assuming a heavy tailed distribution of the stock prices return. We use a stochastic maximum principle to formulate the dynamic optimisation problem. The equations which we obtain does not have any explicit analytical solution, so we look for accurate approximations to estimate the value function and optimal strategy. As our calibration strategy is non-parametric in nature, no prior knowledge on the form of the distribution function is needed. We also provide detailed empirical illustration using real life data. Our results show close concordance with financial intuition.We expect that our results will add to the arsenal of the high frequency traders.