An investor faced with a contingent claim may eliminate risk by (super-) hedging in a financial market. As this is often quite expensive, we study partial hedges which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal...

A new model of a financial market is introduced extending the multidimensional Black-Scholes model to the case where several assets can interact with each other even in the absence of noise. Sufficient conditions for the existence of the equivalent martingale measure, absence of arbitrage and...

In a complete financial market every contingent claim can be hedged perfectly. In an incomplete market it is possible to stay on the safe side by superhedging. But such strategies may require a large amount of initial capital. Here we study the question what an investor can do who is unwilling...

Recently, various authors proposed Monte-Carlo methods for the computation of American option prices, based on least squares regression. The purpose of this paper is to analyze an algorithm due to Longstaff and Schwartz. This algorithm involves two types of approximation. Approximation one:...

Asset prices discounted by a tradable numeraire N should be (local) martingales under some measure Q that is equivalent to the original probability measure P. Instead of studying the set of equivalent martingale measures with respect to a prespecified numeraire, we will look for a tradable...

Let $X$ be an ${\Bbb R}^d$-valued special semimartingale on a probability space $(\Omega , {\cal F} , ({\cal F} _t)_{0 \leq t \leq T} ,P)$ with canonical decomposition $X=X_0+M+A$. Denote by $G_T(\Theta )$ the space of all random variables $(\theta \cdot X)_T$, where $\theta $ is a predictable...

The information dynamics in finance and insurance applications is usually modelled by a filtration. This paper looks at situations where information restrictions apply so that the information dynamics may become non-monotone. A fundamental tool for calculating and managing risks in finance and...

We consider a government that aims at reducing the debt-to-(gross domestic product) (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly observe the development of the underlying macroeconomic...

We show that the sequential closure of a family of probability measures on the canonical space of càdlàg paths satisfying Stricker’s uniform tightness condition is a weak∗ compact set of semimartingale measures in the dual pairing of bounded continuous functions and Radon measures, that...

In a market with transaction costs, generally, there is no nontrivial portfolio that dominates a contingent claim. Therefore, in such a market, preferences have to be introduced in order to evaluate the prices of options. The main goal of this article is to quantify this dependence on...