Approximate share in Portfolio Model

HARK/ConsumptionSaving/ConsPortfolioModel.py

@@ -213,7 +213,7 @@ def update_solution_terminal(self):
         None
         """
         # Consume all market resources: c_T = m_T
-        cFuncAdj_terminal = IdentityFunction()
+        cFuncAdj_terminal = LinearInterp([0.0, 1.0], [0.0, 1.0])
         cFuncFxd_terminal = IdentityFunction(i_dim=0, n_dims=2)
 
         # Risky share is irrelevant-- no end-of-period assets; set to zero
@@ -244,6 +244,8 @@ def update_solution_terminal(self):
             dvdsFuncFxd=dvdsFuncFxd_terminal,
         )
 
+        self.solution_terminal.EndOfPrdShareFunc = ShareFuncAdj_terminal
+
     def update_ShareGrid(self):
         """
         Creates the attribute ShareGrid as an evenly spaced grid on [0.,1.], using
@@ -822,6 +824,74 @@ def make_ShareFuncAdj(self):
         Construct the risky share function when the agent can adjust
         """
 
+        # Share function on aGrid
+
+        if self.zero_bound:
+            aNrm_temp = np.append(0.0, self.aNrmGrid)
+            share_temp = np.append(self.ShareLimit, self.Share_now)
+        else:
+            aNrm_temp = self.aNrmGrid
+            share_temp = self.Share_now
+
+        self.EndOfPrdShareFunc = LinearInterp(
+            aNrm_temp, share_temp, intercept_limit=self.ShareLimit, slope_limit=0.0
+        )
+
+        # alternative share functions from linear approximation
+
+        # get next period's consumption and share function
+        cFunc_next = self.solution_next.cFuncAdj
+        sFunc_next = self.solution_next.EndOfPrdShareFunc
+
+        def premium(shock):
+            """
+            Used to evaluate mean and variance of equity premium.
+            """
+            r_diff = shock - self.Rfree
+
+            return r_diff, r_diff ** 2
+
+        prem_mean, prem_var = calc_expectation(self.RiskyDstn, premium)
+
+        def c_nrm_and_deriv(shocks, a_nrm):
+            """
+            Used to calculate expected consumption and MPC given today's savings,
+            assuming that today's risky share is the same as it would be tomorrow
+            with that same level of savings.
+            """
+            p_shk = shocks[0] * self.PermGroFac
+            share = sFunc_next(a_nrm)
+            r_diff = shocks[2] - self.Rfree
+            r_port = self.Rfree + r_diff * share
+            m_nrm_next = a_nrm * r_port / p_shk + shocks[1]
+
+            c_next, cP_next = cFunc_next.eval_with_derivative(m_nrm_next)
+
+            return c_next, cP_next
+
+        c_vals = calc_expectation(self.ShockDstn, c_nrm_and_deriv, self.aNrmGrid)
+
+        c_vals = c_vals[:, :, 0]
+        c_next = c_vals[0]
+        cP_next = c_vals[1]
+
+        MPC = cP_next * self.aNrmGrid / c_next
+
+        approx_share = prem_mean / (self.CRRA * MPC * prem_var)
+
+        # clip at 0 and 1, although we know the Share limit we
+        # want to see what the approximation would give us
+        approx_share = np.clip(approx_share, 0, 1)
+
+        self.ApproxShareFunc = LinearInterp(
+            self.aNrmGrid,
+            approx_share,
+            intercept_limit=self.ShareLimit,
+            slope_limit=0.0,
+        )
+
+        # Share function for mGrid
+
         if self.zero_bound:
             Share_lower_bound = self.ShareLimit
         else:
@@ -978,6 +1048,9 @@ def make_porfolio_solution(self):
             AdjPrb=self.AdjustPrb,
         )
 
+        self.solution.EndOfPrdShareFunc = self.EndOfPrdShareFunc
+        self.solution.ApproxShareFunc = self.ApproxShareFunc
+
     def solve(self):
         """
         Solve the one period problem for a portfolio-choice consumer.
@@ -1319,10 +1392,7 @@ def add_SequentialShareFuncAdj(self, solution):
             Share_now = self.Share_now
 
         self.SequentialShareFuncAdj_now = LinearInterp(
-            aNrm_temp,
-            Share_now,
-            intercept_limit=self.ShareLimit,
-            slope_limit=0.0,
+            aNrm_temp, Share_now, intercept_limit=self.ShareLimit, slope_limit=0.0,
         )
 
         solution.SequentialShareFuncAdj = self.SequentialShareFuncAdj_now