Browsing by Author "Øksendal, Bernt"
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A Donsker delta functional approach to optimal insider control and applications to finance
Draouil, Olfa; Øksendal, Bernt (Journal article; 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 ... 
A Maximum Principle Approach to Risk Indifference Pricing with Partial Information
An, Ta Thi Kieu; Øksendal, Bernt; Proske, Frank (Peer reviewed, 2008)We consider the problem of risk indifference pricing on an incomplete market, namely on a jump diffusion market where the controller has limited access to market information. We use the maximum principle for stochastic ... 
An anticipative linear filtering equation
Aase, Knut K.; Bjuland, Terje; Øksendal, Bernt (Discussion paper, Working paper, 201008) 
A general stochastic calculus approach to insider trading
Biagini, Francesca; Øksendal, Bernt (Discussion paper, Working paper, 200212)The purpose of this paper is to present a general stochastic calculus approach to insider trading. In a market driven by a standard Brownian motion B(t) on a filtered probability space (Ω, F, {F}t>0, P), by an insider we ... 
Insider trading with partially informed traders
Aase, Knut K.; Bjuland, Terje; Øksendal, Bernt (Discussion paper;2011:21, Working paper, 201111)The single auction equilibrium of Kyle's (1985) is studied, in which noise traders may be partially informed, or alternatively they can be manipulated. Unlike Kyle's assumption that the quantity traded by the noise ... 
Optimal consumption and portfolio in a jump diffusion market
Framstad, Nils Christian; Øksendal, Bernt; Sulem, Agnès (Discussion paper, Working paper, 200106)We consider the problem of optimal consumption and portfolio in a jump diffusion market consisting of a bank account and a stock, whose price is modeled by a geometric Lévy process. We show that in the absence of transaction ... 
Optimal control of predictive meanfield equations and applications to finance
Øksendal, Bernt; Sulem, Agnès (Peer reviewed; Journal article, 2016)We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process X(t) and a predictive ... 
Optimal control of systems with noisy memory and BSDEs with Malliavin derivatives
Øksendal, Bernt; Mohammed, SalahEldin; Røse, Elin Engen; Dahl, Kristina Rognlien (Journal article; Peer reviewed, 2016)In this article we consider a stochastic optimal control problem where the dynamics of the state process, X(t), is a controlled stochastic differential equation with jumps, delay and noisy memory. The term noisy memory ... 
Optimal control with partial information for stochastic Volterra equations
Øksendal, Bernt; Zhang, Tusheng (Journal article; Peer reviewed, 2010)In the first part of the paper we obtain existence and characterizations of an optimal control for a linear quadratic control problem of linear stochastic Volterra equations. In the second part, using the Malliavin calculus ... 
Optimal control with partial information for stochastic Volterra equations
Øksendal, Bernt; Zhang, Tusheng (Journal article; Peer reviewed, 2010)In the first part of the paper we obtain existence and characterizations of an optimal control for a linear quadratic control problem of linear stochastic Volterra equations. In the second part, using the Malliavin ... 
Optimal multidimensional stochastic harvesting with densitydependent prices
Alvarez, Luis H.; Lungu, Edward; Øksendal, Bernt (Journal article; Peer reviewed, 2016)We prove a verification theorem for a class of singular control problems which model optimal harvesting with densitydependent prices or optimal dividend policy with capitaldependent utilities. The result is applied to ... 
A short introduction to mathematical finance
Øksendal, Bernt (Discussion paper, Working paper, 1998)We give a brief survey of some fundamental concepts, methods and results in the mathematics of finance. The survey covers the 3 topics Chapter 1: Markets and arbitrages. The oneperiod model. The multiperiod model. The ... 
Stackelberg equilibria in continuous newsvendor models with uncertain demand and delayed information
Øksendal, Bernt; Sandal, Leif Kristoffer; Ubøe, Jan (Journal article; Peer reviewed, 2014)We consider explicit formulae for equilibrium prices in a continuoustime vertical contracting model. A manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits. Demand ... 
Stochastic Stackelberg equilibria with applications to time dependent newsvendor models
Sandal, Leif Kristoffer; Øksendal, Bernt; Ubøe, Jan (Discussion paper, Working paper, 201105) 
Stochastic Stackelberg equilibria with applications to timedependent newsvendor models
Øksendal, Bernt; Sandal, Leif Kristoffer; Ubøe, Jan (Journal article; Peer reviewed, 2013)In this paper, we prove a maximum principle for general stochastic differential Stackelberg games, and apply the theory to continuous time newsvendor problems. In the newsvendor problem, a manufacturer sells goods to a ... 
Strategic insider trading equilibrium : a filter theory approach
Aase, Knut K.; Bjuland, Terje; Øksendal, Bernt (Discussion paper, Working paper, 201008)The continuoustime version of Kyle's (1985) model of asset pricing with asymmetric information is studied, and generalized in various directions, i.e., by allowing timevarying liquidity trading, and by having weaker ... 
Strategic insider trading equilibrium: A filter theory approach
Aase, Knut K.; Bjuland, Terje; Øksendal, Bernt (Journal article; Peer reviewed, 2012)The continuoustime version of Kyle’s (Econometrica 53(6):1315–1336, 1985 ) model of asset pricing with asymmetric information is studied, and generalized in various directions, i.e., by allowing timevarying liquidity ... 
Strategic insider trading equilibrium : a forward integration approach
Aase, Knut K.; Bjuland, Terje; Øksendal, Bernt (Discussion paper, Working paper, 200711)The continuoustime version of Kyle’s (1985) model of asset pricing with asymmetric information is studied, and generalized in various directions, i.e., by allowing timevarying noise trading, and by allowing the orders ... 
Strategic Insider Trading Equilibrium with a nonfiduciary market maker
Aase, Knut K.; Øksendal, Bernt (Discussion paper;2/19, Working paper, 20190828)The continuoustime version of Kyle's (1985) model is studied, in which market makers are not fiduciaries. They have some market power which they utilize to set the price to their advantage, resulting in positive expected ... 
Strategic Insider Trading in Continuous Time: A New Approach
Aase, Knut K.; Øksendal, Bernt (Discussion paper;3/19, Working paper, 20190829)The continuoustime version of Kyle's (1985) model of asset pricing with asymmetric information is studied, and generalized by allowing timevarying noise trading. From rather simple assumptions we are able to derive the ...