Since its introduction in the early 1980s, the risk-neutral valuation principle has proved to be
an important tool in the pricing and hedging of financial derivatives. Following the success of …

This paper gives an overview of results and developments in the area of pricing and
hedging contingent claims in an incomplete market by means of a quadratic criterion. We …

We summarize recent research in a rapid growing field, that of statistical finance, also called
'econophysics'. There are three main themes in this activity:(i) empirical studies and the …

We propose a new 'hedged'Monte-Carlo (HMC) method to price financial derivatives, which
allows to determine simultaneously the optimal hedge. The inclusion of the optimal hedging …

This paper reports several entirely new results on financial market dynamics and option
pricing. We observe that empirical distributions of returns are much better approximated by …

Estimating and controlling large risks has become one of the main concern of financial
institutions. This requires the development of adequate statistical models and theoretical …

The purpose of this work is to explore the role that random arbitrage opportunities play in
pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio …

The problem of determining the European-style option price in incomplete markets is
examined within the framework of stochastic optimization. An analytic method based on the …

Estimating and controlling large risks has become one of the main concerns of financial
institutions. This requires the development of adequate statistical models and theoretical …

I study the Bouchaud–Sornette, Schweizer and Schäl way of pricing options, presenting the
methodology in accordance with Bouchaud–Sornette. The definitions of the wealth balance …