# Multivalued backward stochastic differential equations with time delayed generators

Bakarime Diomande; Lucian Maticiuc

Open Mathematics (2014)

- Volume: 12, Issue: 11, page 1624-1637
- ISSN: 2391-5455

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topBakarime Diomande, and Lucian Maticiuc. "Multivalued backward stochastic differential equations with time delayed generators." Open Mathematics 12.11 (2014): 1624-1637. <http://eudml.org/doc/269286>.

@article{BakarimeDiomande2014,

abstract = {Our aim is to study the following new type of multivalued backward stochastic differential equation: \[\left\lbrace \{\begin\{array\}\{c\}- dY\left( t \right) + \partial \phi \left( \{Y\left( t \right)\} \right)dt \ni F\left( \{t,Y\left( t \right),Z\left( t \right),Y\_t ,Z\_t \} \right)dt + Z\left( t \right)dW\left( t \right), 0 \leqslant t \leqslant T, \hfill \\ Y\left( T \right) = \xi , \hfill \\ \end\{array\}\} \right.\]
where ∂φ is the subdifferential of a convex function and (Y t, Z t):= (Y(t + θ), Z(t + θ))θ∈[−T,0] represent the past values of the solution over the interval [0, t]. Our results are based on the existence theorem from Delong Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.},

author = {Bakarime Diomande, Lucian Maticiuc},

journal = {Open Mathematics},

keywords = {Backward stochastic differential equations; Time-delayed generators; Subdifferential operator; backward stochastic differential equations; time-delayed generators; subdifferential operator},

language = {eng},

number = {11},

pages = {1624-1637},

title = {Multivalued backward stochastic differential equations with time delayed generators},

url = {http://eudml.org/doc/269286},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Bakarime Diomande

AU - Lucian Maticiuc

TI - Multivalued backward stochastic differential equations with time delayed generators

JO - Open Mathematics

PY - 2014

VL - 12

IS - 11

SP - 1624

EP - 1637

AB - Our aim is to study the following new type of multivalued backward stochastic differential equation: \[\left\lbrace {\begin{array}{c}- dY\left( t \right) + \partial \phi \left( {Y\left( t \right)} \right)dt \ni F\left( {t,Y\left( t \right),Z\left( t \right),Y_t ,Z_t } \right)dt + Z\left( t \right)dW\left( t \right), 0 \leqslant t \leqslant T, \hfill \\ Y\left( T \right) = \xi , \hfill \\ \end{array}} \right.\]
where ∂φ is the subdifferential of a convex function and (Y t, Z t):= (Y(t + θ), Z(t + θ))θ∈[−T,0] represent the past values of the solution over the interval [0, t]. Our results are based on the existence theorem from Delong Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.

LA - eng

KW - Backward stochastic differential equations; Time-delayed generators; Subdifferential operator; backward stochastic differential equations; time-delayed generators; subdifferential operator

UR - http://eudml.org/doc/269286

ER -

## References

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- [2] Łukasz Delong, Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management, preprint, 2011 (http://arxiv.org/abs/1005.4417).
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