## Search

Now showing items 1-100 of 146

(Research report / Forskningsrapport, 2014)

(Research report / Forskningsrapport, 2013)

(Research report / Forskningsrapport, 2013)

We consider a problem of optimal control of an infinite horizon system governed by forward-backward stochastic differential equations with delay. Sufficient and necessary maximum principles for optimal control under partial ...

(Research report / Forskningsrapport, 2013)

We study optimal stochastic control problems of general coupled systems of forward- backward stochastic di erential equations with jumps. By means of the Itô-Ventzell formula the system is transformed to a controlled ...

(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. ...

(Research report / Forskningsrapport, 2012)

We prove maximum principles for the problem of optimal control for a jump diffusion with infinite horizon and partial information. The results are applied to partial information optimal consumption and portfolio problems ...

(Research report / Forskningsrapport, 2011)

(Research report / Forskningsrapport, 2011)

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 traders ...

(Research report / Forskningsrapport, 2011)

We study optimal stochastic control problems under model uncertainty. We rewrite such problems as (zero-sum) stochastic di erential games of forward-backward stochastic di erential equations. We prove general stochastic ...

(Research report / Forskningsrapport, 2011)

(Research report / Forskningsrapport, 2011)

(Research report / Forskningsrapport, 2011)

(Research report / Forskningsrapport, 2011)

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 ...

(Research report / Forskningsrapport, 2010)

(Research report / Forskningsrapport, 2010)

(Research report / Forskningsrapport, 2010)

The continuous-time version of Kyle's [6] model, known as the Back's [2] model, of asset pricing with asymmetric information, is studied. A larger class of price processes and a larger classes of noise traders' processes ...

(Research report / Forskningsrapport, 2010)

(Research report / Forskningsrapport, 2010)

(Research report / Forskningsrapport, 2010)

(Research report / Forskningsrapport, 2010)

(Research report / Forskningsrapport, 2010)

We study partial information, possibly non-Markovian, singular stochastic control of Itô-Lévy processes and obtain general maximum principles. The results are used to find connections between singular stochastic control, ...

(Research report / Forskningsrapport, 2010)

(Research report / Forskningsrapport, 2009)

In this paper we study the Cauchy problem for the wave equation with space-time Lévy noise initial data in the Kondratiev space of stochastic distributions. We prove that this problem has a strong and unique C2-solution, ...

(Research report / Forskningsrapport, 2009)

In this paper we introduce Skorohod-semimartingales as an expanded concept of classical semimartingales in the setting of Lévy processes. We show under mild conditions that Skorohod-semimartingales similarly to semimartingales ...

(Research report / Forskningsrapport, 2009)

We study an optimal stopping problem for a stochastic differential equation with delay driven by a Lévy noise. Approaching the problem by its infinite-dimensional representation, we derive conditions yielding an explicit ...

(Research report / Forskningsrapport, 2009)

In this paper, we study backward stochastic differential equations with respect to general filtrations. The results are used to find the optimal consumption rate for an insider from a cash flow modeled as a generalized ...

(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 ...

(Research report / Forskningsrapport, 2009)

(Research report / Forskningsrapport, 2009)

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 ...

(Research report / Forskningsrapport, 2008)

We present various versions of the maximum principle for optimal control of forward-backward SDEs with jumps. Our study is motivated by risk minimization via g-expectations. We first prove a general sufficient maximum ...

(Research report / Forskningsrapport, 2008)

In this paper we consider a general partial information stochastic differential game where the state process is a controlled Itô-Lévy process. We use Malliavin calculus to derive a maximum principle for general stochastic ...

(Research report / Forskningsrapport, 2008)

This paper considers a controlled Itô-Lévy process the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed ...

(Research report / Forskningsrapport, 2008)

(Research report / Forskningsrapport, 2007)

In this paper we first deal with the problem of optimal control for zero-sum stochastic differential games. We give a necessary and sufficient maximum principle for that problem with partial information. Then we use the ...

(Research report / Forskningsrapport, 2007)

The continuous-time version of Kyle's (1985) model of asset pricing with asymmetric information is studied, and generalized in various directions, i.e., by allowing time-varying noise trading, and by allowing the orders ...

(Research report / Forskningsrapport, 2007)

We give a short introduction to the white noise theory for multiparameter Lévy processes and its application to stochastic partial differential equations driven by such processes. Examples include temperature distribution ...

(Research report / Forskningsrapport, 2007)

(Research report / Forskningsrapport, 2007)

(Research report / Forskningsrapport, 2006)

We study a stochastic control problem where the state process is described by a stochastic differential equation driven by a Brownian motion and a Poisson random measure, being affine in both the state and the control. The ...

(Research report / Forskningsrapport, 2006)

We use white noise calculus for Lévy processes to obtain a representation formula for the functionals of a jump diffusion. Then we use this to find an explicit formula for the Donsker delta function of a jump diffusion and ...

(Research report / Forskningsrapport, 2006)

We study the problem of optimal control of a jump diffusion, i.e. a process which is the solution of a stochastic differential equation driven by Lévy processes. It is required that the control process is adapted to a given ...

(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 ...

(Research report / Forskningsrapport, 2006)

In a market driven by Lévy processes, we consider an optimal portfolio problem for a dealer who has access to some information in general smaller than the one generated by the market events, in this sense we refer to this ...

(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 ...

(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 ...

(Research report / Forskningsrapport, 2005)

In this paper we consider the problem to find a market portfolio that minimizes the convex risk measure of the terminal wealth in a jump diffusion market. We formulate the problem as a two player (zero-sum) stochastic ...

(Research report / Forskningsrapport, 2005)

We present an optimal portfolio problem with logarithmic utility in the following 3 cases:
\begin{itemize}
\item[(i)] The classical case, with complete information from the market available to the agent at all times. ...

(Research report / Forskningsrapport, 2005)

We study impulse control problems of jump diffusions with delayed reaction. This means that there is a delay $\delta>0$ between the time when a decision for intervention is taken and the time when the intervention is ...

(Research report / Forskningsrapport, 2004)

In this paper we obtain existence and uniqueness of solutions of forward stochastic differential equations driven by compensated Poisson random measures. To this end, an Itô-Ventzell formula for jump processes is proved ...

(Research report / Forskningsrapport, 2004)

We study a general optimal stopping problem for a strong Markov process in the case when there is a time lag $\delta>0$ from the time $\tau$ when the decision to stop is taken (a stopping time) to the time $\tau+\delta$ ...

(Research report / Forskningsrapport, 2004)

In this paper we first study the problem of minimal hedging for an insider trader in incomplete markets. We use the forward integral in order to model the insider portfolio and consider a general larger filtration. We ...

(Research report / Forskningsrapport, 2004)

(Research report / Forskningsrapport, 2004)

We consider the forward integral with respect to fractional Brownian motion B(H)(t) and relate this to the Wick-Itô-Skorohod integral by using the M-operator introduced by [10] and the Malliavin derivative DHt. Using this ...

(Research report / Forskningsrapport, 2004)

(Research report / Forskningsrapport, 2003)

(Research report / Forskningsrapport, 2003)

We study the optimal portfolio problem for an insider, in the case that the performance is measured in terms of the logarithm of the terminal wealth minus a term measuring the roughness and the growth of the portfolio. We ...

(Research report / Forskningsrapport, 2003)

We give an explicit formula for the Donsker delta function of a certain class of Lévy processes in the Lévy-Hida distribution space. As an application we use the Donsker delta function to derive an explicit chaos expansion ...

(Research report / Forskningsrapport, 2003)

No abstract

(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 ...

(Research report / Forskningsrapport, 2003)

(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 ...

(Research report / Forskningsrapport, 2002)

In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Lévy white noise. As an example we use this theory to solve the stochastic ...

(Research report / Forskningsrapport, 2002)

We develop a white noise theory for Poisson random measures associated with a Lévy process. The starting point of this theory is a chaos expansion with kernels of polynomial type. We use this to construct the white noise ...

(Research report / Forskningsrapport, 2002)

We discuss the extension to the multi-dimensional case of the Wick-Itô integral with respect to fractional Brownian motion, introduced by [DHP] in the 1-dimensional case. We prove a multi-dimensional Itô type isometry for ...

(Research report / Forskningsrapport, 2002)

(Research report / Forskningsrapport, 2002)

(Research report / Forskningsrapport, 2002)

(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 ...

(Research report / Forskningsrapport, 2001)

We give a short introduction to some of the theory and methods involved in We prove a verification theorem for a class of singular control problems which model optimal harvesting with density-dependent prices or optimal ...

(Research report / Forskningsrapport, 2001)

We give a short introduction to some of the theory and methods involved in stochastic control with partial observation. As an illustration we use the stochastic maximum principle and the Kalman-Bucy filter to solve explicitly ...

(Research report / Forskningsrapport, 2001)

We prove an existence and uniqueness result for a general class of backward stochastic partial differential equations. This is a type of equations which appear as adjoint equations in the maximum principle approach to ...

(Research report / Forskningsrapport, 2001)

We give a verification theorem by employing Arrow's generalization of the Mangasarian sufficient condition to a general jump diffusion setting, and show the adjoint processes' connections to dynamic programming. The result ...

(Research report / Forskningsrapport, 2001)

(Research report / Forskningsrapport, 2001)

We prove a sufficient maximum principle for the optimal control of systems described by a quasilinear stochastic heat equation. The result is applied to give a maximum principle solution method for stochastic control ...

(Research report / Forskningsrapport, 2001)

A Meyer-Tanaka formula involving weighted local time is derived for fractional Brownian motion and geometric fractional Brownian motion. The formula is applied to the study of the stop-loss-start-gain (SLSG) portfolio in ...

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 2000)

Multiparameter fractional Brownian motion and quasi-linear stochastic partial differential equations

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 2000)

Date of this version: 9 December 1999

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 2000)

Date of this version: 22 November 2000

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 1999)

(Research report / Forskningsrapport, 1999)

(Research report / Forskningsrapport, 1999)

(Research report / Forskningsrapport, 1999)

(Research report / Forskningsrapport, 1999)

(Research report / Forskningsrapport, 1999)

(Research report / Forskningsrapport, 1999)

(Research report / Forskningsrapport, 1999)

(Research report / Forskningsrapport, 1999)

(Research report / Forskningsrapport, 1999)

(Research report / Forskningsrapport, 1998)

(Research report / Forskningsrapport, 1998)