Cutting Plane Algorithms for Nonlinear Semi-Definite Programming Problems with Applications
Journal of Global Optimization
Journal of Computational and Applied Mathematics - Special issue: Papers presented at the 1st Sino--Japan optimization meeting, 26-28 October 2000, Hong Kong, China
Tight Bounds On Expected Order Statistics
Probability in the Engineering and Informational Sciences
A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions
Mathematics of Operations Research
The MSOM Society Student Paper Competition: Extended Abstracts of 2005 Winners
Manufacturing & Service Operations Management
A Robust Optimization Approach to Inventory Theory
Operations Research
A semidefinite optimization approach to the steady-state analysis of queueing systems
Queueing Systems: Theory and Applications
Bounding Probability of Small Deviation: A Fourth Moment Approach
Mathematics of Operations Research
Robust Approximation to Multiperiod Inventory Management
Operations Research
Exploiting equalities in polynomial programming
Operations Research Letters
Duality in option pricing based on prices of other derivatives
Operations Research Letters
The truncated Stieltjes moment problem solved by using kernel density functions
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
The idea of investigating the relation of option and stock prices based just on the no-arbitrage assumption, but without assuming any model for the underlying price dynamics, has a long history in the financial economics literature. We introduce convex and, in particular semidefinite optimization methods, duality, and complexity theory to shed new light on this relation. For the single stock problem, given moments of the prices of the underlying assets, we show that we can find best-possible bounds on option prices with general payoff functions efficiently, either algorithmically (solving a semidefinite optimization problem) or in closed form. Conversely, given observable option prices, we provide best-possible bounds on moments of the prices of the underlying assets, as well as on the prices of other options on the same asset by solving linear optimization problems. For options that are affected by multiple stocks either directly (the payoff of the option depends on multiple stocks) or indirectly (we have information on correlations between stock prices), we find nonoptimal bounds using convex optimization methods. However, we show that it is NP-hard to find best possible bounds in multiple dimensions. We extend our results to incorporate transactions costs.