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Now showing items 1-54 of 54
(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)
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 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)
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 / 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, 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 / 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, 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)
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)
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 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)
(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 ...
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 ...
(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)
(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 ...
(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 / 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 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, 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, 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)
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)
(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)
(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)
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)