update a few missing cases

Author: HumphreyYang

lectures/markov_jump_lq.md

@@ -549,7 +549,7 @@ for i, state_var in enumerate(state_vec1):
     ax.plot(λ_vals, F1[:, i], label=r"$\overline{s}_1$", color="b")
     ax.plot(λ_vals, F2[:, i], label=r"$\overline{s}_2$", color="r")
 
-    ax.set_xlabel("$\lambda$")
+    ax.set_xlabel(r"$\lambda$")
     ax.set_ylabel("$F_{s_t}$")
     ax.set_title(f"Coefficient on {state_var}")
     ax.legend()
@@ -617,8 +617,8 @@ for i, state_var in enumerate(state_vec1):
     ax.plot_surface(λ_grid, δ_grid, F1_grid[:, :, i], color="b")
     # low adjustment cost, red surface
     ax.plot_surface(λ_grid, δ_grid, F2_grid[:, :, i], color="r")
-    ax.set_xlabel("$\lambda$")
-    ax.set_ylabel("$\delta$")
+    ax.set_xlabel(r"$\lambda$")
+    ax.set_ylabel(r"$\delta$")
     ax.set_zlabel("$F_{s_t}$")
     ax.set_title(f"coefficient on {state_var}")
     plt.show()
@@ -659,8 +659,8 @@ def run(construct_func, vals_dict, state_vec):
         ax.plot(λ_vals, F1[:, i], label=r"$\overline{s}_1$", color="b")
         ax.plot(λ_vals, F2[:, i], label=r"$\overline{s}_2$", color="r")
 
-        ax.set_xlabel("$\lambda$")
-        ax.set_ylabel("$F(\overline{s}_t)$")
+        ax.set_xlabel(r"$\lambda$")
+        ax.set_ylabel(r"$F(\overline{s}_t)$")
         ax.set_title(f"coefficient on {state_var}")
         ax.legend()
         plt.show()
@@ -681,10 +681,10 @@ def run(construct_func, vals_dict, state_vec):
         # Plot a vertical line at λ=0.5
         ax.plot([0.5, 0.5], [min(k_star), max(k_star)], "-.")
 
-        ax.set_xlabel("$\lambda$")
+        ax.set_xlabel(r"$\lambda$")
         ax.set_ylabel("$k$")
         ax.set_title("Optimal k levels and k targets")
-        ax.text(0.5, min(k_star)+(max(k_star)-min(k_star))/20, "$\lambda=0.5$")
+        ax.text(0.5, min(k_star)+(max(k_star)-min(k_star))/20, r"$\lambda=0.5$")
         ax.legend(bbox_to_anchor=(1., 1.))
         plt.show()
 
@@ -714,9 +714,9 @@ def run(construct_func, vals_dict, state_vec):
         ax = fig.add_subplot(111, projection='3d')
         ax.plot_surface(λ_grid, δ_grid, F1_grid[:, :, i], color="b")
         ax.plot_surface(λ_grid, δ_grid, F2_grid[:, :, i], color="r")
-        ax.set_xlabel("$\lambda$")
-        ax.set_ylabel("$\delta$")
-        ax.set_zlabel("$F(\overline{s}_t)$")
+        ax.set_xlabel(r"$\lambda$")
+        ax.set_ylabel(r"$\delta$")
+        ax.set_zlabel(r"$F(\overline{s}_t)$")
         ax.set_title(f"coefficient on {state_var}")
         plt.show()
 ```

lectures/opt_tax_recur.md

@@ -1242,7 +1242,7 @@ for ax, title, plot in zip(axes, titles, [tax_policy, interest_rate]):
     ax.set(title=title, xlim=(min(gov_debt), max(gov_debt)))
     ax.grid()
 
-axes[0].legend(('Time $t=0$', 'Time $t \geq 1$'))
+axes[0].legend(('Time $t=0$', r'Time $t \geq 1$'))
 axes[1].set_xlabel('Initial Government Debt')
 
 fig.tight_layout()

lectures/rob_markov_perf.md

@@ -469,7 +469,7 @@ The function's code is as follows
 def nnash_robust(A, C, B1, B2, R1, R2, Q1, Q2, S1, S2, W1, W2, M1, M2,
                  θ1, θ2, beta=1.0, tol=1e-8, max_iter=1000):
 
-    """
+    r"""
     Compute the limit of a Nash linear quadratic dynamic game with
     robustness concern.