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Preface Lévy processes are an excellent tool for modelling price processes in mathematical finance. On the one hand, they are very flexible, since for any time increment ∆t any infinitely divisible distribution can be chosen as the increment distribution over periods of time ∆t. On the other hand, they have a simple structure in comparison with general(More)
We derive general necessary and sufficient conditions for the mutual consistency of a given parametrized family of forward rate curves and the dynamics of a given interest rate model. Consistency in this context means that the interest rate model will produce forward rate curves belonging to the parameterized family. The interest rate model may be driven by(More)
We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points. For a general controlled Markov process and a fairly general(More)
We investigate the term structure of zero coupon bonds when interest rates are driven by a general marked point process as well as by a Wiener process. Developing a theory which allows for measure-valued trading portfolios we study existence and uniqueness of a martingale measure. We also study completeness and its relation to the uniqueness of a martingale(More)
We consider a Markovian factor model consisting of a vector price process for traded assets as well as a multidimensional random process for non traded factors. All processes are allowed to be driven by a general marked point process (representing discrete jump events) as well as by a standard multidimensional standard Wiener process. Within this framework(More)
for useful discussions. We are also grateful for comments from Abstract Our objective is to identify the trading strategy that would allow an investor to take advantage of " excessive " stock price volatility and " sentiment " fluctuations. We construct a general-equilibrium model of sentiment. In it, there are two classes of agents and stock prices are(More)
In some recent papers (Elliott and van der Hoek, 2003; Hu and Øksendal, 2003) a fractional Black-Scholes model have been proposed as an improvement of the classical Black-Scholes model (see also Benth, 2003; Biagini et al., 2002; Biagini and Øksendal, 2004). Common to these fractional BlackScholes models, is that the driving Brownian motion is replaced by a(More)
The object of this paper is to study the mean–variance portfolio optimization in continuous time. Since this problem is time inconsistent we attack it by placing the problem within a game theoretic framework and look for subgame perfect Nash equilibrium strategies. This particular problem has already been studied in [2] where the authors assumed a constant(More)
We consider interest rate models where the forward rates are allowed to be driven by a multidimensional Wiener process as well as by a marked point process. Assuming a deterministic volatility structure, and using ideas from systems and control theory, we investigate when the inputoutput map generated by such a model can be realized by a finite dimensional(More)