ﻻ يوجد ملخص باللغة العربية
We present a general framework for portfolio risk management in discrete time, based on a replicating martingale. This martingale is learned from a finite sample in a supervised setting. The model learns the features necessary for an effective low-dimensional representation, overcoming the curse of dimensionality common to function approximation in high-dimensional spaces. We show results based on polynomial and neural network bases. Both offer superior results to naive Monte Carlo methods and other existing methods like least-squares Monte Carlo and replicating portfolios.
When applying Value at Risk (VaR) procedures to specific positions or portfolios, we often focus on developing procedures only for the specific assets in the portfolio. However, since this small portfolio risk analysis ignores information from assets
We propose some machine-learning-based algorithms to solve hedging problems in incomplete markets. Sources of incompleteness cover illiquidity, untradable risk factors, discrete hedging dates and transaction costs. The proposed algorithms resulting s
We extend the classical risk minimization model with scalar risk measures to the general case of set-valued risk measures. The problem we obtain is a set-valued optimization model and we propose a goal programming-based approach with satisfaction fun
The goal of this paper is to investigate the method outlined by one of us (PR) in Cherubini et al. (2009) to compute option prices. We name it the SINC approach. While the COS method by Fang and Osterlee (2009) leverages the Fourier-cosine expansion
In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black-Scholes dynamics. The proposed techniques, called G