An investment horizon is in practice not frequently known with certainty at the initial investment date. This paper addresses the problem of pricing and hedging a random cash‡ow received at a random date in a general stochastic environment. We ...rst argue that speci...c timing risk is induced by the presence of an uncertain time-horizon if and only if the random time under consideration is not...

We introduce a new measure notion on small complexity classes (called F -measure), based on martingale families, that gets rid of some drawbacks of previous measure notions: it can be used to define dimension because martingale families can make money on all strings, and it yields random sequences with an equal frequency of 0’s and 1’s. As applications to F -measure, we answer a question raised...

We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous Lévy processes. With a view of option pricing, we provide a systematic analysis of the existence of equivalent martingale measures, under which the model remains analytically tractable. This includes the existence of Esscher martingale measures and martingale measu...

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 martingale. We then discuss the extension to local risk-minimization when X is a semimartingale and explai...

We give a necessary and sufficient condition on a sequence of functions on a set Ω under which there is a measure on Ω which renders the given sequence of functions a martingale. Further such a measure is unique if we impose a natural maximum entropy condition on the conditional probabilities.

We prove that for continuous stochastic processes S based on ((; F; P) for which there is an equivalent martingale measure Q 0 with square-integrable density dQ 0 =dPwe have that the so-called "variance optimal" martingale measure Q opt for which the density dQ opt =dPhas minimal L 2 (P)-norm is automatically equivalent to P. The result is then applied to an approximation problem arising in Mat...

We prove that for continuous stochastic processes S based on ( ;F;P) for which there is an equivalent martingale measureQ with square-integrable density dQ=dPwe have that the so-called "variance optimal" martingale measure Q for which the density dQ=dPhas minimal L(P)-norm is automatically equivalent to P. The result is then applied to an approximation problem arising in Mathematical Finance.

In a two-period financial market where stock is traded dynamically and European options at maturity are statically, we study the so-called martingale Schrödinger bridge $Q_{*}$ , that is, minimal-entropy measure among all models calibrated to option prices. This minimisation shown be in duality with an exponential utility maximisation over semistatic portfolios. Under technical condition on phy...

This article proposes a model for stock prices which incorporates shot-noise effects. This means, that sudden jumps in the stock price are allowed, but their effect may decline as time passes by. Our model is general enough to capture arbitrary effects of this type. Generalizing previous approaches to shot-noise we in particular allow the decay to be stochastic. This model describes an incomple...

In an incomplete Brownian-motion market setting, we propose a convex monotonic pricing functional for nonattainable bounded contingent claims which is compatible with prices for attainable claims. The pricing functional is defined as the convex conjugate of a generalized entropy penalty functional and an interpretation in terms of tracking with instantaneously vanishing risk can be given. 1. In...