Optimal partial hedging in a discrete-time market as a knapsack problem

TL;DR

This paper introduces a novel approach to optimal partial hedging of European options in discrete-time markets by formulating it as a knapsack problem, enhancing understanding of hedging strategies under constraints.

Contribution

It models partial hedging problems as knapsack problems, providing new insights and a linear programming perspective on discrete-time optimal hedging.

Findings

Partial hedging strategies can be formulated as knapsack problems.

This approach offers a new understanding of hedging under constraints.

The method connects financial hedging with well-studied optimization techniques.

Abstract

We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the expected shortfall under a cost constraint and show that these problems can be treated as so called knapsack problems, which are a widely researched subject in linear programming. This observation gives us better understanding of the problem of optimal hedging in discrete time.