TY - JOUR

T1 - On the Gradient Method in One Portfolio Management Problem

AU - Kumacheva, S.

AU - Novgorodtcev, V.

N1 - Export Date: 21 October 2024 Адрес для корреспонденции: Kumacheva, S.; Department of Economics, Russian Federation; эл. почта: s.kumacheva@spbu.ru Адрес для корреспонденции: Novgorodtcev, V.; Department of Applied Mathematics and Control Processes, Russian Federation; эл. почта: st056062@student.spbu.ru

PY - 2024/10/2

Y1 - 2024/10/2

N2 - This study refines the methodology for solving stochastic optimal control problems with quality criteria that include the sum of the quality functional of the classical formulation and an extremal measure. A two-level optimization solution of these kinds of problems is presented already for the case where the quality functional consists only of the extremal measure. Our study shows the possibility of solving the original time inconsistency problem through solving a two-level optimization problem, where the outer problem is solved by gradient methods since the value function is convex and the inner problem is solved by classical methods. Some experiments were carried out and confirmed the validity of the theory. The results of the study can be applied to the case of portfolio management with quality criteria containing the Conditional Value-at-Risk (CVaR) metric. © 2024 by the authors.

AB - This study refines the methodology for solving stochastic optimal control problems with quality criteria that include the sum of the quality functional of the classical formulation and an extremal measure. A two-level optimization solution of these kinds of problems is presented already for the case where the quality functional consists only of the extremal measure. Our study shows the possibility of solving the original time inconsistency problem through solving a two-level optimization problem, where the outer problem is solved by gradient methods since the value function is convex and the inner problem is solved by classical methods. Some experiments were carried out and confirmed the validity of the theory. The results of the study can be applied to the case of portfolio management with quality criteria containing the Conditional Value-at-Risk (CVaR) metric. © 2024 by the authors.

KW - CVaR (expected shortfall)

KW - portfolio management

KW - stochastic optimal control

KW - time inconsistency

KW - viscosity solution

UR - https://www.mendeley.com/catalogue/bc8a1aba-ed61-3cb0-b602-1be72650551c/

U2 - 10.3390/math12193086

DO - 10.3390/math12193086

M3 - статья

VL - 12

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 19

M1 - 3086

ER -