G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,a...G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,and can be applied to large portfolios of several hundred dimensions with low computational cost.We also apply G-VaR to robust portfolio optimization,thereby providing a tractable means to facilitate optimal allocations under the condition of market ambiguity.展开更多
Model uncertainty is a type of inevitable financial risk.Mistakes on the choice of pricing model may cause great financial losses.In this paper we investigate financial markets with mean-volatility uncertainty.Models ...Model uncertainty is a type of inevitable financial risk.Mistakes on the choice of pricing model may cause great financial losses.In this paper we investigate financial markets with mean-volatility uncertainty.Models for stock market and option market with uncertain prior distributions are established by Peng’s G-stochastic calculus.On the hedging market,the upper price of an(exotic)option is derived following the Black–Scholes–Barenblatt equation.It is interesting that the corresponding Barenblatt equation does not depend on mean uncertainty of the underlying stocks.Appropriate definitions of arbitrage for super-and sub-hedging strategies are presented such that the super-and sub-hedging prices are reasonable.In particular,the condition of arbitrage for sub-hedging strategy fills the gap of the theory of arbitrage under model uncertainty.Finally we show that the term K of finite variance arising in the superhedging strategy is interpreted as the max Profit&Loss(P&L)of shorting a delta-hedged option.The ask-bid spread is in fact an accumulation of the superhedging P&L and the sub-hedging P&L.展开更多
基金supported by Natural Science Foundation of China and Jiangsu Province(No.11871050,No.11971342,No.11401414,No.BK20140299,No.14KJB110022)。
文摘G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,and can be applied to large portfolios of several hundred dimensions with low computational cost.We also apply G-VaR to robust portfolio optimization,thereby providing a tractable means to facilitate optimal allocations under the condition of market ambiguity.
基金The author was supported by the National Natural Science Foundation of China(No.11401414)the National Natural Science Foundation of Jiangsu Province(Nos.BK20140299 and 14KJB110022).
文摘Model uncertainty is a type of inevitable financial risk.Mistakes on the choice of pricing model may cause great financial losses.In this paper we investigate financial markets with mean-volatility uncertainty.Models for stock market and option market with uncertain prior distributions are established by Peng’s G-stochastic calculus.On the hedging market,the upper price of an(exotic)option is derived following the Black–Scholes–Barenblatt equation.It is interesting that the corresponding Barenblatt equation does not depend on mean uncertainty of the underlying stocks.Appropriate definitions of arbitrage for super-and sub-hedging strategies are presented such that the super-and sub-hedging prices are reasonable.In particular,the condition of arbitrage for sub-hedging strategy fills the gap of the theory of arbitrage under model uncertainty.Finally we show that the term K of finite variance arising in the superhedging strategy is interpreted as the max Profit&Loss(P&L)of shorting a delta-hedged option.The ask-bid spread is in fact an accumulation of the superhedging P&L and the sub-hedging P&L.
