Browsing Matematisk institutt by Author "Øksendal, Bernt"
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Draouil, Olfa; Øksendal, Bernt (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2015)We study optimal insider control problems, i.e., optimal control problems of stochastic systems where the controller at any time t, in addition to knowledge about the history of the system up to this time, also has additional ...

Øksendal, Bernt; Sulem, Agnès (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2016)A celebrated financial application of convex duality theory gives an explicit relation between the following two quantities: (i) The optimal terminal wealth X^*(T) : = X_{\varphi ^*}(T) of the problem to maximize the ...

Gjerde, Jon; Holden, Helge; Øksendal, Bernt; Ubøe, Jan; Zhang, Tusheng (Research report / Forskningsrapport, 1994)

Bañuelos, Rodrigo; Øksendal, Bernt (Research report / Forskningsrapport, 1986)

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 ...

Øksendal, Bernt (Research report / Forskningsrapport, 1987)

Øksendal, Bernt (Research report / Forskningsrapport, 1983)

Martio, Olli; Øksendal, Bernt (Research report / Forskningsrapport, 1994)

Biagini, Francesca; Øksendal, Bernt (Research report / Forskningsrapport, 2004)We consider the forward integral with respect to fractional Brownian motion B(H)(t) and relate this to the WickItôSkorohod integral by using the Moperator introduced by [10] and the Malliavin derivative DHt. Using this ...

Øksendal, Bernt; Sulem, Agnès (Research report / Forskningsrapport, 2011)We study optimal stochastic control problems under model uncertainty. We rewrite such problems as (zerosum) stochastic di erential games of forwardbackward stochastic di erential equations. We prove general stochastic ...

Øksendal, Bernt; Sulem, Agnès (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2014)We study optimal stochastic control problems with jumps under model uncertainty. We rewrite such problems as stochastic differential games of forward–backward stochastic differential equations. We prove general stochastic ...

Øksendal, Bernt (Research report / Forskningsrapport, 2003)We give a survey of the stochastic calculus of fractional Brownian motion, and we discuss its applications to financial markets where the prices are described as solutions of stochastic differential equations driven by ...

Yaozhong, Hu; Øksendal, Bernt (Research report / Forskningsrapport, 1999)

Øksendal, Bernt; Sulem, Agnès (Research report / Forskningsrapport, 2006)We consider a stochastic differential game in a financial jump diffusion market, where the agent chooses a portfolio which maximizes the utility of her terminal wealth, while the market chooses a scenario (represented by ...

General fractional multiparameter white noise theory and stochastic partial differential equations. Hu, Yaozhong; Øksendal, Bernt; Zhang, Tusheng (Research report / Forskningsrapport, 2002)

Øksendal, Bernt; Zhang, Tusheng (Research report / Forskningsrapport, 1995)

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 ...

Biagini, Francesca; Øksendal, Bernt (Research report / Forskningsrapport, 2002)

Agram, Nacira; Øksendal, Bernt (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)The classical maximum principle for optimal stochastic control states that if a control û is optimal, then the corresponding Hamiltonian has a maximum at u=û. The first proofs for this result assumed that the control did ...

Brekke, Kjell Arne; Øksendal, Bernt (Research report / Forskningsrapport, 1990)