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Föllmer, Hans; Leukert, Peter - 1998

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...

Persistent link: https://www.econbiz.de/10009574876

A note on stochastic volatility, GARCH models, and hyperbolic distributions

Jaschke, Stefan R. - 1997

We establish a relation between stochastic volatility models and the class of generalized hyperbolic distributions. These distributions have been found to fit exceptionally well to the empirical distribution of stock returns. We review the background of hyperbolic distributions and prove...

Persistent link: https://www.econbiz.de/10009577459

Canonical decomposition of linear transformations of two independent Brownian motions

Föllmer, Hans; Wu, Ching-Tang; Yor, Marc - 1998

filtering theory ; enlargement of filtration ; canonical decomposition ; Sturm-Liouville equation ; Volterra kernels …

Persistent link: https://www.econbiz.de/10009578007

Efficient hedging : cost versus shortfall risk

Föllmer, Hans; Leukert, Peter - 1999

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...

Persistent link: https://www.econbiz.de/10009579176

Higher order forward rate agreements and the smoothness of the term structure

Jaschke, Stefan R. - 1998

This paper proposes linear higher order conditions on the term structure that allow to compute valuation bounds for any deterministic cash stream. Starting from bounds on the forward rate curve and its derivatives, which are nonlinear in the discount factors, we derive linear conditions that are...

Persistent link: https://www.econbiz.de/10009579185

On Itô's formula for multidimensional Brownian motion

Föllmer, Hans; Protter, Philip E. - 2001

Consider a d-dimensional Brownian motion X (Xl, ... ,Xd ) and a function F which belongs locally to the Sobolev space W 1,2. We prove an extension of Ito's formula where the usual second order terms are replaced by the quadratic covariations [fk(X), Xkj involving the weak first partial...

Persistent link: https://www.econbiz.de/10009616778

Convex measures of risk and trading constraints

Föllmer, Hans; Schied, Alexander - 2001

We introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in Artzner et aL (1999), and we prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case...

Persistent link: https://www.econbiz.de/10009615426

Coherent risk measures, valuation bounds, and (my,p)-portfolio optimization

Jaschke, Stefan R.; Küchler, Uwe - 1999

This paper presents a general theory that works out the relation between coherent risk measures, valuation bounds, and … theory presented seems to fill a gap between arbitrage valuation on the one hand and single agent utility maximization or … full-fledged equilibrium theory on the other hand. "Coherent" valuation bounds strike a balance in that the bounds can be …

Persistent link: https://www.econbiz.de/10009581108

On weak Brownian motions of arbitrary order

Föllmer, Hans; Wu, Ching-Tang; Yor, Marc - 1999

We show the existence, for any k E N, of processes which have the same k-marginals as Brownian motion, although they are not Brownian motions. For k = 4, this proves a conjecture of Stoyanov. The law P' of such a "weak Brownian motion of order k" can be constructed to be equivalent to Wiener...

Persistent link: https://www.econbiz.de/10009582418

Convergence of locally and globally interacting Markov chains

Föllmer, Hans; Horst, Ulrich - 2001

We study the long run behaviour of interactive Markov chains on infinite product spaces. In view of microstructure models of financial markets, the interaction has both a local and a global component. The convergence of such Markov chains is analyzed on the microscopic level and on the...

Persistent link: https://www.econbiz.de/10009613614