In this paper,a derivative pricing model in ambiguity market was established via indifferent pricing principle and the backward stochastic differential equation description for the worst case utility in ambiguity mark...
In this paper,a derivative pricing model in ambiguity market was established via indifferent pricing principle and the backward stochastic differential equation description for the worst case utility in ambiguity market in Chen and Epstein [Econometrica,70(2002),1403-1443].Under some proper assumptions,it was proved that the buying price and the selling price in this model are same as the price in the standard Black -Scholes model if no investment restriction exists in the *** if short selling is prohibited in the market,then the selling price or the buying price is different from the price in the B-S model,and it is governed by a forward-backward stochastic differential *** Markovian frame,we transformed the FBSDE into a PDE problem,and compare the prices of European derivatives or American derivatives in this model with the price in B-S model by PDE ***,we use the previous method to establish a convertible bond pricing model in ambiguity market,which can be described as a non-zero-sum Dynkin game problem,and transformed into a variational inequality *** properties of the price and the optimal calling or converting strategies are discovered by PDE method.
It is well known that in the classical single-period mean-variance model,the effcient frontier with both risky and riskless assets is tangent to the efficient frontier with only risky *** means that the inclusion of a...
It is well known that in the classical single-period mean-variance model,the effcient frontier with both risky and riskless assets is tangent to the efficient frontier with only risky *** means that the inclusion of a riskless asset does not increase the highest Sharpe ratio in the single-period *** this paper,we prove that the multi-period mean-variance efficient frontier generated by both risky and riskless assets is strictly separated from the one generated by only risky assets,more specifically,there exists a gap between the two efficient frontiers with and without a riskless *** also prove that the inclusion of a riskless asset strictly enhances the best Sharpe ratio of the efficient frontier in the multi-period setting,and offer an explicit expression for the enhancement of the best Sharpe *** findings show that,in contrast to the single-period mean-variance model,the multi-period mean-variance model includes a number of different structures and ***,a numerical example is provided to illustrate the results obtained in this paper.
The Markowitz mean-variance optimization procedure is highly appreciated as a theoretical result in ***,it has been demonstrated to be less applicable in *** portfolio formed by using the classical Mean-Variance appro...
The Markowitz mean-variance optimization procedure is highly appreciated as a theoretical result in ***,it has been demonstrated to be less applicable in *** portfolio formed by using the classical Mean-Variance approach always resultsin extreme portfolio weights that fluctuate substantially over time and perform poorly in the out-of-sample *** reason for this problem is due to the substantial estimation error of the inputs of the optimization *** classical mean-variance approach which uses the sample mean and sample covariance matrix as inputs always results in serious *** large dimensional data analysis,we prove that the plug-in return is larger than the theoretical optimal return when the dimension of the population goes to infinity with same order of the sample *** phenomenon is called “over-prediction” by Bai,Liu,Wong (2009) in which they advise a bootstrap -corrected estimation to improve the plug-in estimation in the optimal return *** compared with the plug-in estimation,the performance of the bootstrap-corrected estimation is not satisfied in the optimal allocation and the corresponding *** is because in the bootstrap-corrected estimation they still use the sample covariance matrix as the estimation of the population covariance.
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