We study a quadratic BSDE in a continuous filtration with an unbounded generatorand an infinite time horizon. This equation comes from a stochasticcontrol problem in the context of robust utility maximisation.[...]

We consider backward stochastic dierential equations (BSDEs) witha particular quadratic generator and study the behaviour of their solu-tions when the probability measure is changed, the ltration is shrunk,or the underlying probability space is transformed.[...]

We study the exponential utility indifference valuation of a contingentclaim H when asset prices are given by a general semimartingale S. Under mildassumptions on H and S, we prove that a no-arbitrage type condition is fulfilled ifand only if H has a certain representation. In this case, the...

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...

An equivalent !-martingale measure (E!MM) for a given stochastic process Sis a probability measure R equivalent to the original measure P such that S isan R-!-martingale. Existence of an E!MM is equivalent to a classical absenceof-arbitrage property of S, and is invariant if we replace the...

We propose a new approach to the pricing and hedging of contingent claims under transaction costs in a general incomplete market in discrete time. Under the assumptions of a bounded mean-variance tradeoff, substantial risk and a nondegeneracy condition on the conditional variances of asset...