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...

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...

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 this paper two kinds of cumulant processes are studied in a general setting. These processes generalize the cumulant of an infinitely divisible random variable and they appear as the exponential compensator of a semimartingale. In a financial context cumulant processes lead to a generalized...

We use the Cox process (or a doubly stochastic Poisson process) to model the claim arrival process for catastrophic events. The shot noise process is used for the claim intensity function within the Cox process. The Cox process with shot noise intensity is examined by piecewise deterministic...

This paper considers the problem of pricing discrete barrier options. A discrete barrier option is a barrier option where the barrier is monitored only at specific dates. This paper continues the work initiated by Broadie et al. in [B-G-K] and determine formulas to estimate the price of discrete...

In the present paper we show how to extend any time-homogeneous short-rate model to a model that can reproduce any observed yield curve, through a procedure that preserves the possible analytical tractability of the original model. In the case of the Vasicek (1977) model, our extension is...

We propose a new model for pricing of bonds and their options based on the short rate when the latter exhibits a step function like behaviour. The model produces realistic looking spot rate curves, and allows one to derive explicit formulae for the yield curve and put and cap options. This model...

We consider a diffusion type model for the short rate, where the drift and diffusion parameters are modulated by an underlying Markov process. The underlying Markov process is assumed to have a stochastic differential driven by Wiener processes and a marked point process. The model for the short...

Stochastic flows and their Jacobians are used to show why, when the short rate process is described by Gaussian dynamics, (as in the Vasicek or Hull-White models), or square root, affine (Bessel) processes, (as in the Cox-Ingersoll-Ross, or Duffie-Kan models), the bond price is an exponential...