Peter Lindberg: "The knapsack problem approach in solving partial hedging problems of options"
August 31, 2012 Andreas Lundell PhD theses
This thesis introduces a new approach for studying the problem of optimal partial hedging of both European and American options in a finite and complete discrete-time market model. We show how certain partial hedging problems, that have been treated earlier using other methods, can alternatively be reduced to different types of knapsack problems, which are a well known subject in the field of linear programming. We also pose two new partial hedging problems for American options and solve them as knapsack problems.
The main focus is on hedging problems, where optimality is measured in terms of success probability. In these cases the problems are reduced to knapsack problems of a 0-1 type, which in turn can be solved approximately using a so called greedy algorithm. We show how the greedy algorithm can be implemented efficiently in a binomial model.
The thesis can be downloaded here.