Shortfall Risk Minimization in Discrete Time Financial Market Models

作     者：Frikha, N. 

作者机构：Univ Paris Diderot LPMA F-75205 Paris France 

出 版 物：《SIAM JOURNAL ON FINANCIAL MATHEMATICS》 (SIAM金融数学杂志)

年 卷 期：2014年第5卷第1期

页      面：384-414页

核心收录：

学科分类：1202[管理学-工商管理] 07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：shortfall risk measures risk minimization dynamic programming principle stochastic approximation algorithm vector quantization Monte Carlo simulation 

摘      要：In this paper, we study theoretical and computational aspects of risk minimization in financial market models operating in discrete time. To define the risk, we consider a class of convex risk measures defined on L-p(P) in terms of shortfall risk. Under mild assumptions, namely, the absence of arbitrage opportunity and the nondegeneracy of the price process, we prove the existence of an optimal strategy by performing a dynamic programming argument in a non-Markovian framework. In a Markovian framework, the shortfall risk and optimal dynamic strategies are estimated using three main tools: Newton-Raphson Monte Carlo-based procedure, stochastic approximation algorithm, and Markovian quantization scheme. Finally, we illustrate our approach by considering several shortfall risk measures and portfolios inspired by energy and financial markets.