kth.sePublications
Change search
Link to record
Permanent link

Direct link
Agram, Nacira, Associate professorORCID iD iconorcid.org/0000-0003-1662-0215
Publications (10 of 24) Show all publications
Agram, N., Pucci, G. & Øksendal, B. (2024). Impulse Control of Conditional McKean–Vlasov Jump Diffusions. Journal of Optimization Theory and Applications, 200(3), 1100-1130
Open this publication in new window or tab >>Impulse Control of Conditional McKean–Vlasov Jump Diffusions
2024 (English)In: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 200, no 3, p. 1100-1130Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider impulse control problems involving conditional McKean–Vlasov jump diffusions, with the common noise coming from the σ-algebra generated by the first components of a Brownian motion and an independent compensated Poisson random measure. We first study the well-posedness of the conditional McKean–Vlasov stochastic differential equations (SDEs) with jumps. Then, we prove the associated Fokker–Planck stochastic partial differential equation (SPDE) with jumps. Next, we establish a verification theorem for impulse control problems involving conditional McKean–Vlasov jump diffusions. We obtain a Markovian system by combining the state equation with the associated Fokker–Planck SPDE for the conditional law of the state. Then we derive sufficient variational inequalities for a function to be the value function of the impulse control problem, and for an impulse control to be the optimal control. We illustrate our results by applying them to the study of an optimal stream of dividends under transaction costs. We obtain the solution explicitly by finding a function and an associated impulse control, which satisfy the verification theorem.

Place, publisher, year, edition, pages
Springer Nature, 2024
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-346045 (URN)10.1007/s10957-023-02370-6 (DOI)001144857000001 ()2-s2.0-85182649962 (Scopus ID)
Funder
Swedish Research Council, 2020-04697KTH Royal Institute of Technology
Note

QC 20240502

Available from: 2024-05-01 Created: 2024-05-01 Last updated: 2024-05-02Bibliographically approved
Agram, N. & Øksendal, B. (2024). Optimal stopping of conditional McKean–Vlasov jump diffusions. Systems & control letters (Print), 188, Article ID 105815.
Open this publication in new window or tab >>Optimal stopping of conditional McKean–Vlasov jump diffusions
2024 (English)In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 188, article id 105815Article in journal (Refereed) Published
Abstract [en]

The purpose of this paper is to study the optimal stopping problem of conditional McKean–Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean–Vlasov jump diffusions, for short). We obtain sufficient variational inequalities for a function to be the value function of such a problem and for a stopping time to be optimal.

The key is that we combine the conditional McKean–Vlasov equation with the associated stochastic Fokker–Planck partial integro-differential equation for the conditional law of the state. This leads to a Markovian system which can be handled by using a version of a Dynkin formula.

Our verification result is illustrated by finding the optimal time to sell in a market with common noise and jumps.

Place, publisher, year, edition, pages
Elsevier BV, 2024
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-346047 (URN)10.1016/j.sysconle.2024.105815 (DOI)2-s2.0-85191661714 (Scopus ID)
Funder
Swedish Research Council, 2020-04697
Note

QC 20240502

Available from: 2024-05-01 Created: 2024-05-01 Last updated: 2024-05-14Bibliographically approved
Makhlouf, K., Agram, N., Hilbert, A. & oksendal, B. (2023). SPDEs with space interactions and application to population modelling. ESAIM: Control, Optimisation and Calculus of Variations , 29, Article ID 18.
Open this publication in new window or tab >>SPDEs with space interactions and application to population modelling
2023 (English)In: ESAIM: Control, Optimisation and Calculus of Variations , ISSN 1292-8119, E-ISSN 1262-3377, Vol. 29, article id 18Article in journal (Refereed) Published
Abstract [en]

We consider optimal control of a new type of non-local stochastic partial differential equations (SPDEs). The SPDEs have space interactions, in the sense that the dynamics of the system at time t and position in space x also depend on the space-mean of values at neighbouring points. This is a model with many applications, e.g. to population growth studies and epidemiology. We prove the existence and uniqueness of strong, smooth solutions of a class of SPDEs with space interactions, and we show that, under some conditions, the solutions are positive for all times if the initial values are. Sufficient and necessary maximum principles for the optimal control of such systems are derived. Finally, we apply the results to study an optimal vaccine strategy problem for an epidemic by modelling the population density as a space-mean stochastic reaction-diffusion equation.

Place, publisher, year, edition, pages
EDP Sciences, 2023
Keywords
Stochastic partial differential equations (SPDEs), strong, smooth solutions, space interactions, spacemean dependence, population modelling, maximum principle, backward stochastic partial differential equations (BSPDEs), space-mean stochastic reaction diffusion equation, optimal vaccination strategy
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-325243 (URN)10.1051/cocv/2023010 (DOI)000942919500001 ()2-s2.0-85149676992 (Scopus ID)
Note

QC 20230404

Available from: 2023-04-04 Created: 2023-04-04 Last updated: 2023-08-24Bibliographically approved
Agram, N. & Øksendal, B. (2023). Stochastic Fokker-Planck equations for conditional McKean-Vlasov jump diffusions and applications to optimal control. SIAM Journal of Control and Optimization, 61(3), 1472-1493
Open this publication in new window or tab >>Stochastic Fokker-Planck equations for conditional McKean-Vlasov jump diffusions and applications to optimal control
2023 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 61, no 3, p. 1472-1493Article in journal (Refereed) Published
Abstract [en]

The purpose of this paper is to study optimal control of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffu-sions, for short). To this end, we first prove a stochastic Fokker-Planck equation for the conditional law of the solution of such equations. Combining this equation with the original state equation, we obtain a Markovian system for the state and its conditional law. Furthermore, we apply this to formulate a Hamilton-Jacobi-Bellman equation for the optimal control of conditional McKean-Vlasov jump diffusions. Then we study the situation when the law is absolutely continuous with respect to Lebesgue measure. In that case the Fokker-Planck equation reduces to a stochastic par-tial differential equation for the Radon-Nikodym derivative of the conditional law. Finally we apply these results to solve explicitly the linear-quadratic optimal control problem of conditional stochastic McKean-Vlasov jump diffusions, and optimal consumption from a cash flow.

Place, publisher, year, edition, pages
Society for Industrial & Applied Mathematics (SIAM), 2023
Keywords
jump diffusion, common noise, conditional McKean-Vlasov differential equation, stochastic Fokker-Planck equation, optimal control, HJB equation
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-334288 (URN)10.1137/21M1461034 (DOI)001031998600016 ()2-s2.0-85163551831 (Scopus ID)
Note

QC 20231122

Available from: 2023-08-18 Created: 2023-08-18 Last updated: 2023-11-22Bibliographically approved
Agram, N. & Øksendal, B. (2023). The Donsker delta function and local time for McKean–Vlasov processes and applications. Stochastics: An International Journal of Probablitiy and Stochastic Processes, 1-18
Open this publication in new window or tab >>The Donsker delta function and local time for McKean–Vlasov processes and applications
2023 (English)In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, p. 1-18Article in journal (Refereed) Published
Abstract [en]

The purpose of this paper is to establish a stochastic differential equation for the Donsker delta measure of the solution of a McKean–Vlasov (mean-field) stochastic differential equation. If the Donsker delta measure is absolutely continuous with respect to Lebesgue measure, then its Radon–Nikodym derivative is called the Donsker delta function. In that case it can be proved that the local time of such a process is simply the integral with respect to time of the Donsker delta function. Therefore we also get an equation for the local time of such a process. For some particular McKean–Vlasov processes, we find explicit expressions for their Donsker delta functions and hence for their local times. 

Place, publisher, year, edition, pages
Informa UK Limited, 2023
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-346046 (URN)10.1080/17442508.2023.2286252 (DOI)001115160100001 ()2-s2.0-85179971272 (Scopus ID)
Funder
Swedish Research Council, 2020-04697
Note

QC 20240502

Available from: 2024-05-01 Created: 2024-05-01 Last updated: 2024-05-02Bibliographically approved
Agram, N., Hu, Y. & oksendal, B. (2022). Mean-field backward stochastic differential equations and applications. Systems & control letters (Print), 162, Article ID 105196.
Open this publication in new window or tab >>Mean-field backward stochastic differential equations and applications
2022 (English)In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 162, article id 105196Article in journal (Refereed) Published
Abstract [en]

In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of the form & nbsp;& nbsp;{dY(t) = -[alpha(1)(t)Y(t) +& nbsp;beta(1)(t)Z(t) +& nbsp;integral(R0 & nbsp;)eta(1)(t,& nbsp;zeta)K(t,& nbsp;zeta)nu(d zeta) +& nbsp;alpha(2)(t)E[Y(t)] +& nbsp;beta(2)(t)E[Z(t)] +& nbsp;integral(R0 & nbsp;)eta(2)(t,& nbsp;zeta)E[K(t,& nbsp;zeta)]nu(d zeta) +& nbsp;gamma(t)]dt + Z(t)dB(t) +& nbsp;integral K-R0 (t,& nbsp;zeta)(N) over tilde(dt, d zeta), t & nbsp;is an element of & nbsp;[0, T].Y(T) =xi.& nbsp;& nbsp;where (Y, Z, K) is the unknown solution triplet, B is a Brownian motion, (N) over tilde is a compensated Poisson random measure, independent of B. We prove the existence and uniqueness of the solution triplet (Y, Z, K) of such systems. Then we give an explicit formula for the first component Y(t) by using partial Malliavin derivatives. To illustrate our result we apply them to study a mean-field recursive utility optimization problem in finance.

Place, publisher, year, edition, pages
Elsevier BV, 2022
Keywords
<p>Mean-field backward stochastic differential equations</p>, Existence and uniqueness, Linear mean-field BSDE, Explicit solution, Mean-field recursive utility problem
National Category
Probability Theory and Statistics Mathematical Analysis Other Mathematics
Identifiers
urn:nbn:se:kth:diva-312195 (URN)10.1016/j.sysconle.2022.105196 (DOI)000788749000012 ()2-s2.0-85126959192 (Scopus ID)
Note

QC 20220518

Available from: 2022-05-18 Created: 2022-05-18 Last updated: 2022-06-25Bibliographically approved
Agram, N., Haadem, S., Øksendal, B. & Proske, F. (2022). Optimal Stopping, Randomized Stopping, and Singular Control with General Information Flow. Theory of Probability and its Applications, 66(4), 601-612
Open this publication in new window or tab >>Optimal Stopping, Randomized Stopping, and Singular Control with General Information Flow
2022 (English)In: Theory of Probability and its Applications, ISSN 0040-585X, E-ISSN 1095-7219, Vol. 66, no 4, p. 601-612Article in journal, Editorial material (Refereed) Published
National Category
Natural Sciences
Identifiers
urn:nbn:se:kth:diva-313647 (URN)10.1137/s0040585x97t990642 (DOI)000752423100008 ()2-s2.0-85129821707 (Scopus ID)
Note

QC 20220620

Available from: 2022-06-09 Created: 2022-06-09 Last updated: 2024-03-18Bibliographically approved
Agram, N., Labed, S., Oksendal, B. & Yakhlef, S. (2022). Singular Control Of Stochastic Volterra Integral Equations. Acta Mathematica Scientia, 42(3), 1003-1017
Open this publication in new window or tab >>Singular Control Of Stochastic Volterra Integral Equations
2022 (English)In: Acta Mathematica Scientia, ISSN 0252-9602, E-ISSN 1003-3998, Vol. 42, no 3, p. 1003-1017Article in journal (Refereed) Published
Abstract [en]

This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations, where the solution X-u,X-xi(t) =X(t) is given by X(t) = phi(t) + integral(t)(0) b (t, s, X(s), u(s)) ds + integral(t)(0) sigma (t, s, X(s), u(s)) dB(s) + integral(t )(0)h (t, s) d xi(s). Here dB(s) denotes the Brownian motion Ito type differential, xi denotes the singular control (singular in time t with respect to Lebesgue measure) and u denotes the regular control (absolutely continuous with respect to Lebesgue measure). Such systems may for example be used to model harvesting of populations with memory, where X(t) represents the population density at time t, and the singular control process xi represents the harvesting effort rate. The total income from the harvesting is represented by J(u, xi) = E[integral(T)(0) f(0)(t, X(t), u(t))dt + integral(T)(0) f(1)(t, X(t))d xi(t) + g(X(T))], for the given functions f(0), f(1) and g, where T > 0 is a constant denoting the terminal time of the harvesting. Note that it is important to allow the controls to be singular, because in some cases the optimal controls are of this type. Using Hida-Malliavin calculus, we prove sufficient conditions and necessary conditions of optimality of controls. As a consequence, we obtain a new type of backward stochastic Volterra integral equations with singular drift. Finally, to illustrate our results, we apply them to discuss optimal harvesting problems with possibly density dependent prices.

Place, publisher, year, edition, pages
Springer Nature, 2022
Keywords
Stochastic maximum principle, stochastic Volterra integral equation, singular control, backward stochastic Volterra integral equation, Hida-Malliavin calculus
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-312209 (URN)10.1007/s10473-022-0311-9 (DOI)000784562000011 ()2-s2.0-85128715046 (Scopus ID)
Note

QC 20220516

Available from: 2022-05-16 Created: 2022-05-16 Last updated: 2022-06-25Bibliographically approved
Agram, N. & Øksendal, B. (2020). A financial market with singular drift and no arbitrage. Mathematics and Financial Economics, 15(3), 477-500
Open this publication in new window or tab >>A financial market with singular drift and no arbitrage
2020 (English)In: Mathematics and Financial Economics, ISSN 1862-9679, E-ISSN 1862-9660, Vol. 15, no 3, p. 477-500Article in journal (Refereed) Published
National Category
Natural Sciences
Identifiers
urn:nbn:se:kth:diva-313648 (URN)10.1007/s11579-020-00284-9 (DOI)000592540200001 ()2-s2.0-85096571698 (Scopus ID)
Funder
The Research Council of Norway, 250768/F20
Note

QC 20220620

Available from: 2022-06-09 Created: 2022-06-09 Last updated: 2024-03-18Bibliographically approved
Agram, N. & Choutri, S. E. (2020). Mean-field FBSDE and optimal control. Stochastic Analysis and Applications, 39(2), 235-251
Open this publication in new window or tab >>Mean-field FBSDE and optimal control
2020 (English)In: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 39, no 2, p. 235-251Article in journal (Refereed) Published
National Category
Natural Sciences
Identifiers
urn:nbn:se:kth:diva-313649 (URN)10.1080/07362994.2020.1794893 (DOI)000553364700001 ()2-s2.0-85088825101 (Scopus ID)
Note

QC 20220620

Available from: 2022-06-09 Created: 2022-06-09 Last updated: 2024-03-18Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-1662-0215

Search in DiVA

Show all publications