The problem of option pricing is treated using the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be mean-reverting. Assuming that only discrete past stock information is available, an interacting...

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Follmer and Schied (2002). The dynamic optimization problem of finding a self-financing...

The paper studies the problem of minimizing coherent risk measures of shortfall for general discrete-time financial models with cone-constrained trading strategies, as developed by Pham and Touzi. It is shown that the optimal strategy is obtained by super-hedging a contingent claim, which is...

This paper concerns questions related to the regulation of liquidity risk, and proposes a definition of an acceptable portfolio. Because the concern is with risk management, the paper considers processes under the physical (rather than the martingale) measure. Basically, a portfolio is...

A model for pricing and hedging in incomplete markets is proposed. This model is derived from expected utility theory, and a connection with the traditional no-arbitrage framework is noted. It is shown that the CGM model can be implemented to value risky assets in incomplete markets.

This paper is concerned with optimal market making in the foreign exchange market. The market maker's holdings in the different currencies are modelled as stochastic processes that are influenced by both the stochastic exchange rates and the stochastic customer buy and sell orders. The market...

The Black-Scholes option pricing methodology requires that the model for the price of the underlying asset be completely specified. Often the underlying price is taken to be a geometric Brownian motion with a constant, known volatility. In practice one does not know precise values of parameters...

Utility based indifference pricing and hedging are now considered to be an economically natural method for valuing contingent claims in incomplete markets. However, acceptance of these concepts by the wide financial community has been hampered by the computational and conceptual difficulty of...

In a discrete setting, a model is developed for pricing a contingent claim in incomplete markets. Since hedging opportunities influence the price of a contingent claim, the optimal hedging strategy is first introduced assuming that a contingent claim has been issued: a strategy implemented by...

Arbitrage theory is used to price forward (futures) contracts in energy markets, where the underlying assets are non-tradeable. The method is based on the so-called 'fitting of the yield curve' technique from interest rate theory. The spot price dynamics of Schwartz is generalized to...