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 first present the approach of risk-minimization in the case where the underlying discounted price process X is a local...

We consider some relations between the minimal martingale measure and the value preserving martingale measure in a continuous-time securities market. Under the assumption of continuous share prices we show that under a structure condition both these martingale measures exist and indeed coincide....

Let X be a continuous adapted process for which there exists an equivalent local martingale measure (ELMM). The minimal martingale measure P is the unique ELMM for X with the property that local P-martingales strongly orthogonal to the P-martingale part of X are also local P-martingales. We...

In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will...

We propose a model for trading in emission allowances in the EU Emission Trading Scheme (ETS). Exploiting an arbitrage relationship we derive the spot prices of carbon allowances given a forward contract whose price is exogenous to the model. The modeling is done under the assumption of no...

We consider option pricing when dynamic portfolios are discretely rebalanced. The portfolio adjustments only occur after fixed relative variation of the stock price. The stock price follows a marked point process and the market is incomplete. We first characterize the equivalent martingale...

This paper presents results on the convergence for hedging strategies in the setting of incomplete financial markets. We examine the convergence of the so-called locally risk-minimizing strategy. It is proved that such a choice for the trading strategy, when perfect hedging of contingent claims...

Let $X$ be a special semimartingale of the form $X=X_0+M+\int d\langle M\rangle\,\widehat\lambda$ and denote by $\widehat K=\int \widehat\lambda^{\rm tr}\,d\langle M\rangle\,\widehat\lambda$ the mean-variance tradeoff process of $X$. Let $\Theta$ be the space of predictable processes $\theta$...

If calibrated to an observed term structure of interest rates that only covers a finite range of times-to-maturity an HJM-model of the term structure of interest rates will eventually die out in finite time as bonds reach maturity. This poses problems for the pricing and hedging of certain...