6 research outputs found
Preliminary remarks on option pricing and dynamic hedging
An elementary arbitrage principle and the existence of trends in financial
time series, which is based on a theorem published in 1995 by P. Cartier and Y.
Perrin, lead to a new understanding of option pricing and dynamic hedging.
Intricate problems related to violent behaviors of the underlying, like the
existence of jumps, become then quite straightforward by incorporating them
into the trends. Several convincing computer experiments are reported.Comment: 1st International Conference on Systems and Computer Science,
Villeneuve d'Ascq : France (2012
Hedging of Financial Derivative Contracts via Monte Carlo Tree Search
The construction of approximate replication strategies for derivative
contracts in incomplete markets is a key problem of financial engineering.
Recently Reinforcement Learning algorithms for pricing and hedging under
realistic market conditions have attracted significant interest. While
financial research mostly focused on variations of -learning, in Artificial
Intelligence Monte Carlo Tree Search is the recognized state-of-the-art method
for various planning problems, such as the games of Hex, Chess, Go,... This
article introduces Monte Carlo Tree Search as a method to solve the stochastic
optimal control problem underlying the pricing and hedging of financial
derivatives. As compared to -learning it combines reinforcement learning
with tree search techniques. As a consequence Monte Carlo Tree Search has
higher sample efficiency, is less prone to over-fitting to specific market
models and generally learns stronger policies faster. In our experiments we
find that Monte Carlo Tree Search, being the world-champion in games like Chess
and Go, is easily capable of directly maximizing the utility of investor's
terminal wealth without an intermediate mathematical theory.Comment: Added figures. Added references. Corrected typos. 15 pages, 5 figure
user's guide to viscosity solutions of second order partial differential equations
The notion of viscosity solutions of scalar fully nonlinear partial
differential equations of second order provides a framework in which startling
comparison and uniqueness theorems, existence theorems, and theorems about
continuous dependence may now be proved by very efficient and striking
arguments. The range of important applications of these results is enormous.
This article is a self-contained exposition of the basic theory of viscosity
solutions.Comment: 67 page