Arbitrage-free interval of American contingent claims under proportional transaction cost

In a general continuous-time market model with proportional transaction costs, we derive the range of arbitrage-free prices of American contingent claims. Using a martingale approach, we obtain the upper and the lower hedging price of American contingent claims.

Mean-variance Hedging for Pricing European-type Contingent Claims with Transaction Costs

In this paper, a European-type contingent claim pricing problem withtransaction costs is considered by a mean-variance hedging argument. The investor has to paytransaction costs which are proportional to the amount of stock transacted. The writer's hedgingobject is to minimize the hedging risk, defined as the variance of hedging error at expiration, witha proper expected excess return level. At first, we consider the mean-variance hedging problem: forinitial hedging wealth f, maximizing the excess expected return under the minimum hedging risklevel V_0. On the other hand, we consider a mean-variance portfolio problem, which is to maximizethe expected return with initial wealth 0 under the same risk level V_0. The minimum initial hedgingwealth f, which can offset the difference of the maximum expected return of these two problems, isthe writer's price.

Hedging Game Contingent Claims with Constrained Portfolios

Game option is an American-type option with added feature that the writer can exercise the option at any time before maturity.In this paper,we consider the problem of hedging Game Contingent Claims(GCC)in two cases.For the case that portfolio is unconstrained,we provide a single arbitrage-free price P_(0).Whereas for the constrained case,the price is replaced by an interval[h_(low),h_(up)]of arbitrage-free prices.And for the portfolio with some closed constraints,we give the expressions of the upper-hedging price and lower-hedging price.Finally,for a special type of game option,we provide explicit expressions of the price and optimal portfolio for the writer and holder.

PRICING AND HEDGING OF AMERICAN CONTINGENT CLAIMS IN INCOMPLETE MARKETS

This paper studies the pricing and hedging for American contingent claims in an incom-plete market under mild conditions using the numeraire method to avoid changes of probabilitymeasure. When the market is incomplete, prices can not be derived by no-arbitrage arguments,since it is not possible to replicate the payoff of a given contingent claim by a controlled portfolioof the basic securitites. We adopt the method of fictitious completion of [1] to provide an upperbound and a lower bound for the actual market price of the claim.

A multidimensional subdiffusion model:An arbitrage-free market

To capture the subdiffusive characteristics of financial markets, the subordinated process, directed by the inverse α-stale subordinator Sα （t） for 0 〈 α〈 1, has been employed as the model of asset prices. In this article, we introduce a multidimensional subdiffusion model that has a bond and K correlated stocks. The stock price process is a multidimen- sional subdiffusion process directed by the inverse a-stable subordinator. This model describes the period of stagnation for each stock and the behavior of the dependency between multiple stocks. Moreover, we derive the multidimensional fractional backward Kolmogorov equation for the subordinated process using the Laplace transform technique. Finally, using a martingale approach, we prove that the multidimensional subdiffusion model is arbitrage-free, and also gives an arbitrage-free pricing rule for contingent claims associated with the martingale measure.