We present a method of hedging Conditional Value at Risk of a position in stock using put options. The result leads to a linear programming problem that can be solved to optimise risk hedging.

American options are priced and hedged in a general discrete market in the presence of arbitrary proportional transaction costs inherent in trading the underlying asset, modelled as bid-ask spreads. Pricing, hedging and optimal stopping algorithms are established for a short position (seller's...

The paper is devoted to optimal superreplication of European options in the discrete setting under proportional transaction costs on the underlying asset. In particular, general pricing and hedging algorithms are developed. This extends previous work by many authors, which has been focused on...

American options exercised by physical delivery of a portfolio of cash and underlying stock are considered in the binary tree model under small proportional transaction costs. Dynamic programming type recursive algorithms are developed for computing the ask and bid prices of such options,...

Dynamic programming algorithms are developed for computing the ask and bid prices of American contingent claims in a binary tree setting in the presence of small proportional transaction costs, extending the recursive construction of the Snell envelope. Associated with the pricing algorithms are...

In the paper by Melnikov and Petrachenko published in Finance and Stochastics 9 (2005), 141--149, a procedure is put forward for pricing and replicating an arbitrary European contingent claim in the binomial market with transaction costs. We present an example to show that the option price...

American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale representations are presented for short (seller's) and long...

The notion of utility maximising entropy (u-entropy) of a probability density, which was introduced and studied by Slomczynski and Zastawniak (Ann. Prob 32 (2004) 2261-2285, arXiv:math.PR/0410115 v1), is extended in two directions. First, the relative u-entropy of two probability measures in...