Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Reprinted from Mathematical Methods in Operations Research (2010), Volume 71, Number 2, 371-399 Terms of use: Documents in AbstractWe consider the problem of maximizing terminal utility in a model where asset prices are driven by Wiener processes, but where the various rates of returns are allowed to be arbitrary semimartingales. The only information available to the investor is the one generated by the asset prices and, in particular, the return processes cannot be observed directly. This leads to an optimal control problem under partial information and for the cases of power, log, and exponential utility we manage to provide a surprisingly explicit representation of the optimal terminal wealth as well as of the optimal portfolio strategy. This is done without any assumptions about the dynamical structure of the return processes. We also show how various explicit results in the existing literature are derived as special cases of the general theory. * Support from the Tom Hedelius and Jan Wallander Foundation is gratefully acknowledged. The authors are very grateful to the Associate editor and two anonymous referees for a number of very helpful comments.
We investigate the term structure of forward and futures prices for models where the price processes are allowed to be driven by a general marked point process as well as by a multidimensional Wiener process. Within an infinite dimensional HJM-type model for futures and forwards we study the properties of futures and forward convenience yield rates. For finite dimensional factor models, we develop a theory of affine term structures, which is shown to include almost all previously known models. We also derive two general pricing formulas for futures options. Finally we present an easily applicable sufficient condition for the possibility of fitting a finite dimensional futures price model to an arbitrary initial futures price curve, by introducing a time dependent function in the drift term.
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 rate thus falls within the category of hidden Markov models.For this model we look at the bond pricing problem. In order to obtain more concrete results we introduce the notion of a semi-affine term structure and give sufficient conditions for the existence of such a term structure. For a special case, when the underlying process is a Markov chain with only two states, we obtain a closed form expression for bond prices.Furthermore we consider the pricing problem when the modulating process can not be directly observed. It turns out that pricing in this context may be viewed as a filtering problem.
Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may March 2001This version: May 6, 2002 AbstractWe consider forward rate rate models of Heath-Jarrow-Morton type, as well as more general infinite dimensional SDEs, where the volatility/diffusion term is stochastic in the sense of being driven by a separate hidden Markov process. Within this framework we use the previously developed Hilbert space realization theory in order provide general necessary and sufficent conditions for the existence of a finite dimensional Markovian realizations for the stochastic volatility models. We illustrate the theory by analyzing a number of concrete examples.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.