Browsing Matematisk institutt by Author "Proske, Frank"
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Di Nunno, Giulia; KohatsuHiga, Arturo; MeyerBrandis, Thilo; Øksendal, Bernt; Proske, Frank; Sulem, Agnès (Research report / Forskningsrapport, 2005)An insider is an agent who has access to larger information than the one given by the development of the market events and who takes advantage of this in optimizing his position in the market. In this paper we consider the ...

ARBITRAGEFREE PRICING DYNAMICS OF INTERESTRATE GUARANTEES BASED ON THE UTILITY INDIFFERENCE METHOD Benth, Fred Espen; Proske, Frank (Research report / Forskningsrapport, 2005)We consider the problem of utility indifference pricing of a put option written on a nontradeable asset, where we can hedge in a correlated asset. The dynamics are assumed to be a twodimensional geometric Brownian motion, ...

Øksendal, Bernt; Proske, Frank; Zhang, Tusheng (Research report / Forskningsrapport, 2005)We prove an existence and uniqueness result for a general class of backward stochastic partial differential equations with jumps. This is a type of equations which appear as adjoint equations in the maximum principle ...

Mandrekar, V.; MeyerBrandis, Thilo; Proske, Frank (Research report / Forskningsrapport, 2007)A Bayes type formula is derived for the nonlinear filter where the observation contains both general Gaussian noise as well as Cox noise whose jump intensity depends on the signal. This formula extends the well know ...

Øksendal, Bernt; Proske, Frank; Signahl, Mikael (Research report / Forskningsrapport, 2009)In this paper we study the Cauchy problem for the wave equation with spacetime Lévy noise initial data in the Kondratiev space of stochastic distributions. We prove that this problem has a strong and unique C2solution, ...

Mataramvura, Sure; Øksendal, Bernt; Proske, Frank (Research report / Forskningsrapport, 2003)We give an explicit formula for the Donsker delta function of a certain class of Lévy processes in the LévyHida distribution space. As an application we use the Donsker delta function to derive an explicit chaos expansion ...

MeyerBrandis, Thilo; Proske, Frank (Research report / Forskningsrapport, 2004)In this paper we present a method to derive explicit representations of strong solutions of forward stochastic differential equations driven by a Brownian motion. These representations open new perspectives in the study ...

Explicit Representation of Strong Solutions of SDE's driven by Infinite Dimensional Lévy Processes MeyerBrandis, Thilo; Proske, Frank (Research report / Forskningsrapport, 2008)We develop a white noise framework for Lévy processes on Hilbert spaces. As the main result of this paper, we then employ the white noise technique to explicitly represent strong solutions of stochastic differential equations ...

Benth, Fred Espen; Di Nunno, Giulia; Løkka, Arne; Øksendal, Bernt; Proske, Frank (Research report / Forskningsrapport, 2001)In a market driven by a Lévy martingale, we consider a claim x. We study the problem of minimal variance hedging and we give an explicit formula for the minimal variance portfolio in terms of Malliavin derivatives. We ...

Explicit Solution of a Nonlinear Filtering Problem for Lévy Processes with Application to Finance MeyerBrandis, Thilo; Proske, Frank (Research report / Forskningsrapport, 2003)In this paper we explicitly solve a nonlinear filtering problem with mixed observations, modelled by a Brownian motion and a generalized Cox process, whose jump intensity is given in terms of a Lévy measure. Motivated by ...

Lanconelli, Alberto; Proske, Frank (Research report / Forskningsrapport, 2003)We give an explicit representation of strong solutions of ItôSDE's in Hilbert spaces in terms of a non linear operation on a stochastic distribution space. This formula can be potentially used to obtain solutions of SDE's ...

MeyerBrandis, Thilo; Proske, Frank; Menoukeu Pamen, Olivier (Research report / Forskningsrapport, 2010)In this paper, we develop a variational approach to study perturbation problems of ordinary differential equations (ODE's) with discontinuous coefficients. We propose a mathematical framework which can be used to construct ...

A general maximum principle for anticipative stochastic control and applications to insider trading Di Nunno, Giulia; Øksendal, Bernt; Menoukeu Pamen, Olivier; Proske, Frank (Research report / Forskningsrapport, 2009)In this paper we suggest a general stochastic maximum principle for optimal control of anticipating stochastic differential equations driven by a Lévy type of noise. We use techniques of Malliavin calculus and forward ...

Løkka, Arne; Proske, Frank (Research report / Forskningsrapport, 2002)We develop a white noise calculus for pure jump Lévy processes on Poisson space. This theory covers the treatment of Lévy processes of unbounded variation. The starting point of the theory is a novel construction of a ...

Di Nunno, Giulia; MeyerBrandis, Thilo; Øksendal, Bernt; Proske, Frank (Research report / Forskningsrapport, 2003)We introduce the forward integral with respect to a pure jump Lévy process and we prove and formula for this integral. Then we use Mallivin calculus to establish a relationship between the forward integral and the Skorohod ...

MeyerBrandis, Thilo; Proske, Frank; Salleh, Hassilah Binti; Menoukeu Pamen, Olivier (Research report / Forskningsrapport, 2007)In this paper we employ Malliavin calculus to derive a general stochastic maximum principle for stochastic partial di¨eremtial equations with jumps under partial information. We apply this result to solve an optimal ...

Flandoli, Franco; Nilssen, Torstein Kastberg; Proske, Frank (Research report / Forskningsrapport, 2013)We consider a class of Hilbertspace valued SDE’s where the drift coefficients are non Lipschitzian in the sense of Höldercontinuity. Using a novel technique based on Malliavin calculus we show in this paper the existence ...

Kettler, Paul C.; Proske, Frank; Yablonski, Aleh (Research report / Forskningsrapport, 2005)The design of this study is to investigate the evolution of a stochastic price process consequent to discrete processes of bids and offers in a market microstructure setting. Under a set of flexible assumptions about agent ...

Øksendal, Bernt; Proske, Frank; Ta, An Thi Kieu (Research report / Forskningsrapport, 2008)

Haadem, Sven; Øksendal, Bernt; Proske, Frank; Agram, Nacira (Research report / Forskningsrapport, 2012)We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. ...