Table 7 Different BSDE drivers for various choices of X and M

1

V̂

V̂

\(-\hat{\mathcal{Z}}_{t}\sigma (t, S_{t})^{-1}(\mu (t, S_{t}) + \operatorname{diag}(\gamma ^{\mathcal{S}}_{t}-q^{\mathcal{S}})S_{t}) + r^{X}_{t} \hat{V_{t}}\)

2

V

V

\(-\hat{\mathcal{Z}}_{t}\sigma (t, S_{t})^{-1}(\mu (t, S_{t}) + \operatorname{diag}(\gamma ^{\mathcal{S}}_{t}-q^{\mathcal{S}})S_{t}) + (r^{\mathcal{B}}_{t} + r^{\mathcal{C}}_{t} - q^{\mathcal{C}}_{t})(V_{t} - \hat{\mathcal{V}}_{t}) + r^{X}_{t} V_{t}\)

3

V

V̂

\(-\hat{\mathcal{Z}}_{t}\sigma (t, S_{t})^{-1}(\mu (t, S_{t}) + \operatorname{diag}(\gamma ^{\mathcal{S}}_{t}-q^{\mathcal{S}})S_{t}) + (r^{\mathcal{B}}_{t} + r^{\mathcal{C}}_{t} - q^{\mathcal{C}}_{t})(V_{t} - \hat{\mathcal{V}}_{t}) + r^{X}_{t} V_{t} +(r^{\mathcal{B}}_{t}+ R^{\mathcal{C}}r^{\mathcal{C}}_{t} - r_{t} - R^{\mathcal{C}}q^{\mathcal{C}}_{t})(\hat{V}_{t} - V_{t})^{+} + [(r^{\mathcal{B}}_{t}-r^{F}_{t})R^{\mathcal{B}}+ r^{\mathcal{C}}_{t}-q^{\mathcal{C}}_{t}](\hat{V}_{t} - V_{t})^{-}\)

4

V̂

V

\(-\hat{\mathcal{Z}}_{t}\sigma (t, S_{t})^{-1}(\mu (t, S_{t}) + \operatorname{diag}(\gamma ^{\mathcal{S}}_{t}-q^{\mathcal{S}})S_{t}) + r^{X}_{t} V_{t} +[(r^{\mathcal{B}}_{t}-r_{t}) + R^{\mathcal{C}}(r^{\mathcal{C}}_{t} - q^{\mathcal{C}}_{t})](V_{t} - \hat{V}_{t})^{+} + [(r^{\mathcal{B}}-r^{F}_{t})R^{\mathcal{B}}+ r^{\mathcal{C}}_{t}-q^{\mathcal{C}}_{t}](V_{t} - \hat{V}_{t})^{-}\)