Abstract
In this paper, we investigate some kind of Dynkin game under g-expectation induced by backward stochastic differential equation (short for BSDE). The lower and upper value functions $$\underline{V}_t=ess\sup \nolimits _{\tau \in {\mathcal {T}_t}} ess\inf \nolimits _{\sigma \in {\mathcal {T}_t}}\mathcal {E}^g_t[R(\tau ,\sigma )]$$
V
̲
t
=
e
s
s
sup
τ
∈
T
t
e
s
s
inf
σ
∈
T
t
E
t
g
[
R
(
τ
,
σ
)
]
and $$\overline{V}_t=ess\inf \nolimits _{\sigma \in {\mathcal {T}_t}} ess\sup \nolimits _{\tau \in {\mathcal {T}_t}}\mathcal {E}^g_t[R(\tau ,\sigma )]$$
V
¯
t
=
e
s
s
inf
σ
∈
T
t
e
s
s
sup
τ
∈
T
t
E
t
g
[
R
(
τ
,
σ
)
]
are defined, respectively. Under some suitable assumptions, a pair of saddle points is obtained and the value function of Dynkin game $$V(t)=\underline{V}_t=\overline{V}_t$$
V
(
t
)
=
V
̲
t
=
V
¯
t
follows. Furthermore, we also consider the constrained case of Dynkin game.
Deep Learning-Based Least Square Forward-Backward Stochastic Differential Equation Solver for High-Dimensional Derivative Pricing
