On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance

Mokhtar Hafayed; Petr Veverka; Syed Abbas

Applications of Mathematics (2014)

  • Volume: 59, Issue: 4, page 407-440
  • ISSN: 0862-7940

Abstract

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We establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by forward-backward stochastic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum condition on the Hamiltonian function is a sufficient condition for near-optimality. At the end, as an application to finance, mean-variance portfolio selection mixed with a recursive utility optimization problem is given.

How to cite

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Hafayed, Mokhtar, Veverka, Petr, and Abbas, Syed. "On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance." Applications of Mathematics 59.4 (2014): 407-440. <http://eudml.org/doc/261933>.

@article{Hafayed2014,
abstract = {We establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by forward-backward stochastic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum condition on the Hamiltonian function is a sufficient condition for near-optimality. At the end, as an application to finance, mean-variance portfolio selection mixed with a recursive utility optimization problem is given.},
author = {Hafayed, Mokhtar, Veverka, Petr, Abbas, Syed},
journal = {Applications of Mathematics},
keywords = {stochastic near-optimal controls; jump processes; forward-backward stochastic systems with jumps; necessary and sufficient conditions for near-optimality; Ekeland's variational principle; stochastic near-optimal controls; jump processes; forward-backward stochastic systems with jumps; necessary and sufficient conditions for near-optimality; Ekeland's variational principle},
language = {eng},
number = {4},
pages = {407-440},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance},
url = {http://eudml.org/doc/261933},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Hafayed, Mokhtar
AU - Veverka, Petr
AU - Abbas, Syed
TI - On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 407
EP - 440
AB - We establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by forward-backward stochastic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum condition on the Hamiltonian function is a sufficient condition for near-optimality. At the end, as an application to finance, mean-variance portfolio selection mixed with a recursive utility optimization problem is given.
LA - eng
KW - stochastic near-optimal controls; jump processes; forward-backward stochastic systems with jumps; necessary and sufficient conditions for near-optimality; Ekeland's variational principle; stochastic near-optimal controls; jump processes; forward-backward stochastic systems with jumps; necessary and sufficient conditions for near-optimality; Ekeland's variational principle
UR - http://eudml.org/doc/261933
ER -

References

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