## Search

Now showing items 1-100 of 187

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2020)

We study a financial market where the risky asset is modelled by a geometric Itô-Lévy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company ...

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2019)

We use a white noise approach to study the problem of optimal insider control of a stochastic delay equation driven by a Brownian motion B and a Poisson random measure N. In particular, we use Hida-Malliavin calculus and ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)

The purpose of this paper is to study the following topics and the relation between them: (i) Optimal singular control of mean-field stochastic differential equations with memory; (ii) reflected advanced mean-field backward ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2019)

We study optimal control of stochastic Volterra integral equations (SVIE) with jumps by using Hida-Malliavin calculus.
We give conditions under which there exist unique solutions of such equations.
Then we prove both a ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)

We consider the problem of optimal singular control of a stochastic partial differential equation (SPDE) with space-mean dependence. Such systems are proposed as models for population growth in a random environment. We ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)

Our purpose of this paper is to study stochastic control problems for systems driven by mean-field stochastic differential equations with elephant memory, in the sense that the system (like the elephants) never forgets its ...

(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 ...

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2018)

In this paper, we study strongly robust optimal control problems under volatility uncertainty. In the G-framework, we adapt the stochastic maximum principle to find necessary and sufficient conditions for the existence of ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2018)

We study optimal control for mean-field stochastic partial differential equations (stochastic evolution equations) driven by a Brownian motion and an independent Poisson random measure, in case of partial information ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)

We study the problem of optimal insider control of an SPDE (a stochastic evolution equation) driven by a Brownian motion and a Poisson random measure. Our optimal control problem is new in two ways:
- The controller has ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)

This article studies singular mean field control problems and singular mean field two-players stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)

By a memory mean-field process we mean the solution X(\cdot ) of a stochastic mean-field equation involving not just the current state X(t) and its law \mathcal {L}(X(t)) at time t, but also the state values X(s) and its ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)

We introduce the concept of singular recursive utility. This leads to a kind of singular backward stochastic differential equation (BSDE) which, to the best of our knowledge, has not been studied before. We show conditions ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2016)

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2016)

We prove a verification theorem for a class of singular control problems which model optimal harvesting with density-dependent prices or optimal dividend policy with capital-dependent utilities. The result is applied to ...

(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 ...

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 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 ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2016)

We study stochastic differential games of jump diffusions, where the players have access to inside information. Our approach is based on anticipative stochastic calculus, white noise, Hida–Malliavin calculus, forward ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2016)

We combine stochastic control methods, white noise analysis, and Hida–Malliavin calculus applied to the Donsker delta functional to obtain explicit representations of semimartingale decompositions under enlargement of ...

(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 ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2015)

Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore, classical methods, such as dynamic programming, cannot be used to study optimal control problems for such equations. However, ...

(Chapter / Bokkapittel / AcceptedVersion; Peer reviewed, 2015)

We present a new approach to the optimal portfolio problem for an insider with logarithmic utility. Our method is based on white noise theory, stochastic forward integrals, Hida-Malliavin calculus and the Donsker delta function.

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2014)

We give a short introduction to the stochastic calculus for Itô-Lévy processes and review briefly the two main methods of optimal control of systems described by such processes:
(i) Dynamic programming and the ...

(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 ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2014)

This paper is mainly a survey of recent research developments regarding methods for risk minimization in financial markets modeled by Itô-Lévy processes, but it also contains some new results on the underlying stochastic ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2014)

We consider a financial market model with a single risky asset whose price process evolves according to a general jump-diffusion with locally bounded coefficients and where market participants have only access to a partial ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2014)

We consider general singular control problems for random fields given by a stochastic partial differential equation (SPDE). We show that under some conditions the optimal singular control can be identified with the solution ...

(Research report / Forskningsrapport, 2014)

Stackelberg equilibria in continuous newsvendor models with uncertain demand and delayed information

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2014)

We consider explicit formulae for equilibrium prices in a continuous-time vertical contracting model. A manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits. Demand is ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2014)

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 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 ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2013)

We study stochastic differential games of jump diffusions driven by Brownian motions and compensated Poisson random measures, where one of the players can choose the stochastic control and the other player can decide when ...

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2013)

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, 2013)

(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 ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 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 ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2013)

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 an optimal consumption and portfolio problem in infinite ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2012)

In this paper, we study backward stochastic differential equations (BSDEs) with respect to general filtrations. We prove existence and uniqueness theorems for such BSDEs and we establish a comparison theorem. Reflected ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2012)

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 ...

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2012)

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, ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2012)

In this paper, we initiate a study on optimal control problem for stochastic differential games under generalized expectation via backward stochastic differential equations and partial information. We first prove a sufficient ...

(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)

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, 2011)

(Research report / Forskningsrapport, 2011)

(Research report / Forskningsrapport, 2011)

(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, 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, 2010)

(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, 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, 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 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)

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 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, 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)

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)

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)

(Research report / Forskningsrapport, 2007)

(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)

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)

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, 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)

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, 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)

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, 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)

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)

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)

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)

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)

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, 2004)

(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)

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, 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)

(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)

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 ...