NDLI: Dynamic Robust Duality in Utility Maximization

Content Provider	Springer Nature Link
Author	Øksendal, Bernt Sulem, Agnès
Copyright Year	2016
Abstract	A celebrated financial application of convex duality theory gives an explicit relation between the following two quantities: (i) The optimal terminal wealth $$X^(T) : = X_{\varphi ^}(T)$$ X ∗ ( T ) : = X φ ∗ ( T ) of the problem to maximize the expected U-utility of the terminal wealth $$X_{\varphi }(T)$$ X φ ( T ) generated by admissible portfolios $$\varphi (t); 0 \le t \le T$$ φ ( t ) ; 0 ≤ t ≤ T in a market with the risky asset price process modeled as a semimartingale; (ii) The optimal scenario $$\frac{dQ^}{dP}$$ d Q ∗ d P of the dual problem to minimize the expected V-value of $$\frac{dQ}{dP}$$ d Q d P over a family of equivalent local martingale measures Q, where V is the convex conjugate function of the concave function U. In this paper we consider markets modeled by Itô-Lévy processes. In the first part we use the maximum principle in stochastic control theory to extend the above relation to a dynamic relation, valid for all $$t \in [0,T]$$ . We prove in particular that the optimal adjoint process for the primal problem coincides with the optimal density process, and that the optimal adjoint process for the dual problem coincides with the optimal wealth process; $$0 \le t \le T$$ . In the terminal time case $$t=T$$ we recover the classical duality connection above. We get moreover an explicit relation between the optimal portfolio $$\varphi ^$$ and the optimal measure $$Q^*$$ . We also obtain that the existence of an optimal scenario is equivalent to the replicability of a related T-claim. In the second part we present robust (model uncertainty) versions of the optimization problems in (i) and (ii), and we prove a similar dynamic relation between them. In particular, we show how to get from the solution of one of the problems to the other. We illustrate the results with explicit examples.
Ending Page	147
Page Count	31
Starting Page	117
File Format	PDF
ISSN	00954616
e-ISSN	14320606
Journal	Applied Mathematics and Optimization
Issue Number	1
Volume Number	75
Language	English
Publisher	Springer US
Publisher Date	2016-01-21
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Backward stochastic differential equation Robust duality Systems Theory, Control Theoretical, Mathematical and Computational Physics Dynamic duality method Robust portfolio optimization Stochastic maximum principle Itô-Lévy market Mathematical Methods in Physics Calculus of Variations and Optimal Control; Optimization Optimal stochastic control Stochastic ordinary differential equations Applications in optimization, convex analysis, mathematical programming, economics Stochastic models Numerical and Computational Physics, Simulation
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Robust Utility Maximization Under Convex Portfolio Constraints

Maximum Principles for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps

Risk minimization in financial markets modeled by Itô-Lévy processes

Sufficient Stochastic Maximum Principle for Discounted Control Problem

Stochastic Maximum Principle for Optimal Control of SPDEs

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

Robust Consumption-Investment Problem on Infinite Horizon

A Stochastic Recursive Optimal Control Problem Under the G-expectation Framework

Maximum principle for forward-backward doubly stochastic control systems and applications

Dynamic Robust Duality in Utility Maximization

Similar Documents

Robust Utility Maximization Under Convex Portfolio Constraints

Maximum Principles for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps

Risk minimization in financial markets modeled by Itô-Lévy processes

Sufficient Stochastic Maximum Principle for Discounted Control Problem

Stochastic Maximum Principle for Optimal Control of SPDEs

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

Robust Consumption-Investment Problem on Infinite Horizon

A Stochastic Recursive Optimal Control Problem Under the G-expectation Framework

Maximum principle for forward-backward doubly stochastic control systems and applications

Dynamic Robust Duality in Utility Maximization