We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and...

This paper studies modelling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for...

This paper studies modelling and existence issues for market models of stochastic implied volatility in a continuous-time framework with one stock, one bank account and a family of European options for all maturities with a fixed payoff function h. We first characterize absence of arbitrage in...

A generalized correlated random walk is a process X_k of partial sums of random variables Y_j such that (X,Y) forms a Markov chain. For a sequence X^n of such processes where each Y^n_j takes only two values, we prove weak convergence to a diffusion process whose generator is explicitly...

We study the dynamic utility indifference value process p(X) when the usefulness of X is evaluated via a dynamic monetary concave utility functional (DMCUF) instead of von Neumann/Morgenstern expected utility. A DMCUF is minus a dynamic convex risk measure. The key tools for our investigations...

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...

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...