The pricing of options for securities markets with delayed response

An approximation scheme for Black-Scholes equations with delays

“…This is the payoff function for the European option considered in [10][11][12]. Note that the reward function λ ∈ C 2 (C) if the function H ∈ C 2,2 (R × R) (i.e., H(x, y) is twice continuously differentiable with respect to x and y).…”

Portfolio theory of optimal isometric force production: Variability predictions and nonequilibrium fluctuation–dissipation theorem

“…(10) by its timedelayed counterpart −γf (t − τ ), where τ denotes a time delay. Such time-delayed dynamical models have recently been discussed in financial physics [43][44][45][46][47] and abound in movement sciences and neurophysics (see e.g. [29,30,39,[48][49][50][51][52][53][54][55][56][57][58][59][60][61] and ref- erences therein).…”

Stochastic Control of Hereditary Systems and Applications

“…36) of which the Black-Scholes (B, S)-market (i.e., f (S(t)) ≡ µ ∈ and g(S(t)) ≡ σ > 0) is a special case. When r > 0, (0.31) is general enough to include the following linear model considered by Chang and Youree [CY99] and pure discrete delay models considered by Arriojas et al [AHMP07] and Kazmerchuk et al [KSW04a,KSW04b,and KSW04c]:…”