Shortfall Risk Approximations for American Options in the multidimensional Black--Scholes Model

We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black--Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path dependent payoffs. In comparison to previous papers we consider the multi assets case for which we use the weak convergence approach

Limit Theorems for Partial Hedging Under Transaction Costs

We study shortfall risk minimization for American options with path dependent payoffs under proportional transaction costs in the Black--Scholes (BS) model. We show that for this case the shortfall risk is a limit of similar terms in an appropriate sequence of binomial models. We also prove that in the continuous time BS model for a given initial capital there exists a portfolio strategy which minimizes the shortfall risk. In the absence of transactions costs (complete markets) similar limit theorems were obtained in Dolinsky and Kifer (2008, 2010) for game options. In the presence of transaction costs the markets are no longer complete and additional machinery required. Shortfall risk minimization for American options under transaction costs was not studied before

Another Correction. Error estimates for Binomial approximations of game options

The Annals of Applied Probability 16 (2006) 984--1033 [URL: http://projecteuclid.org/euclid.aoap/1151592257]Comment: Published in at http://dx.doi.org/10.1214/07-AAP479 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org