Browsing Matematisk institutt by Author "Agram, Nacira"
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Agram, Nacira; Øksendal, Bernt (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)

Agram, Nacira (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)Risk measure is a fundamental concept in finance and in the insurance industry. It is used to adjust life insurance rates. In this article, we will study dynamic risk measures by means of backward stochastic Volterra ...

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 ...

Agram, Nacira; Øksendal, Bernt (Research report / Forskningsrapport, 2013)We consider a problem of optimal control of an infinite horizon system governed by forwardbackward stochastic differential equations with delay. Sufficient and necessary maximum principles for optimal control under partial ...

Agram, Nacira; Øksendal, Bernt (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 ...

Agram, Nacira; Øksendal, Bernt (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, ...

Agram, Nacira; Haadem, Sven; Øksendal, Bernt; Proske, Frank Norbert (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. ...

Haadem, Sven; Øksendal, Bernt; Proske, Frank; Agram, Nacira (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. ...

Agram, Nacira; Øksendal, Bernt (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)Our purpose of this paper is to study stochastic control problems for systems driven by meanfield stochastic differential equations with elephant memory, in the sense that the system (like the elephants) never forgets its ...

Agram, Nacira; Øksendal, Bernt (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)

Agram, Nacira; Øksendal, Bernt; Yakhlef, Samia (Journal article / Tidsskriftartikkel / SubmittedVersion, 2019)We study optimal control of stochastic Volterra integral equations (SVIE) with jumps by using HidaMalliavin calculus. We give conditions under which there exist unique solutions of such equations. Then we prove both a ...

Agram, Nacira; Engen Røse, Elin (Journal article / Tidsskriftartikkel / SubmittedVersion, 2017)We study methods for solving stochastic control problems of systems offorward–backward meanfield equations with delay, in finite and infinite time horizon.Necessary and sufficient maximum principles under partial information ...

Agram, Nacira; Bachouch, Achref; Øksendal, Bernt; Proske, Frank Norbert (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 meanfield stochastic differential equations with memory; (ii) reflected advanced meanfield backward ...

Agram, Nacira; Hilbert, Astrid; Øksendal, Bernt (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)We consider the problem of optimal singular control of a stochastic partial differential equation (SPDE) with spacemean dependence. Such systems are proposed as models for population growth in a random environment. We ...

Jeanblanc, Monique; Agram, Nacira; Lim, Thomas (Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2017)In this paper, we are interested by advanced backward stochastic differential equations (ABSDEs), in a probability space equipped with a Brownian motion and a single jump process, with a jump at time τ. ABSDEs are BSDEs ...

Agram, Nacira; Øksendal, Bernt (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)By a memory meanfield process we mean the solution X(\cdot ) of a stochastic meanfield 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 ...