Updated dependences

.gitignore

@@ -120,3 +120,4 @@ venv.bak/
 
 doc/index - Copy.xrst
 cheat-sheets/preamble.fmt
+*.png

README.rst

@@ -4,13 +4,14 @@
 
 -----
 
-aggregate: a powerful Python actuarial modeling library
-========================================================
+aggregate: a powerful actuarial modeling library
+==================================================
 
 Purpose
 -----------
 
-``aggregate`` solves insurance, risk management, and actuarial problems using realistic models that reflect
+``aggregate`` builds approximations to compound (aggregate) probability distributions quickly and accurately.
+It can be used to solve insurance, risk management, and actuarial problems using realistic models that reflect
 underlying frequency and severity. It delivers the speed and accuracy of parametric distributions to situations
 that usually require simulation, making it as easy to work with an aggregate (compound) probability distribution
 as the lognormal. ``aggregate`` includes an expressive language called DecL to describe aggregate distributions
@@ -47,6 +48,19 @@ Installation
 Version History
 -----------------
 
+
+0.21.3
+~~~~~~~~
+
+* Risk progression, defaults to linear allocation.
+* Added ``g_insurance_statistics`` to ``extensions`` to plot insurance statistics from a distortion ``g``.
+* Added ``g_risk_appetite`` to ``extensions`` to plot risk appetite from a distortion ``g`` (value, loss ratio,
+  return on capital, VaR and TVaR weights).
+* Corrected Wang distortion derivative.
+* Vectorized ``Distortion.g_prime`` calculation for proportional hazard
+* Added ``tvar_weights`` function to ``spectral`` to compute the TVaR weights of a distortion. (Work in progress)
+* Updated dependencies in pyproject.toml file.
+
 0.21.2
 ~~~~~~~~
 
@@ -447,4 +461,4 @@ Social media: https://www.reddit.com/r/AggregateDistribution/.
 
 .. |twitter| image:: https://img.shields.io/twitter/follow/mynl.svg?label=follow&style=flat&logo=twitter&logoColor=4FADFF
     :target: https://twitter.com/SJ2Mi
-    :alt: Twitter Follow
+    :alt: Twitter Follow

aggregate/__init__.py

@@ -20,7 +20,7 @@
                         integral_by_doubling, logarithmic_theta, block_iman_conover,
                         make_var_tvar, test_var_tvar, kaplan_meier, kaplan_meier_np,
                         more, parse_note, parse_note_ex, introspect, explain_validation)
-from .spectral import Distortion, approx_ccoc
+from .spectral import Distortion, approx_ccoc, tvar_weights
 from .distributions import Frequency, Severity, Aggregate
 from .portfolio import Portfolio, make_awkward
 from .underwriter import Underwriter, build
@@ -49,7 +49,7 @@
 __email__ = "steve@convexrisk.com"
 __status__ = "beta"
 # only need to change here, feeds conf.py (docs) and pyproject.toml (build)
-__version__ = "0.21.2"
+__version__ = "0.21.3"
 
 
 

aggregate/bounds.py

@@ -60,8 +60,8 @@ def __init__(self, distribution_spec):
         # hack for beta distribution, you want to force 1 to be in tvar ps, but Fp = 1
         # TODO figure out why p_star grinds to a halt if you input b < inf
         self.add_one = True
-        logger.warning('Deprecatation warning. The kind argument is now ignored. Functionality '
-                       'is equivalent to kind="tail", which was the most accurate method.')
+        # logger.warning('Deprecatation warning. The kind argument is now ignored. Functionality '
+        #                'is equivalent to kind="tail", which was the most accurate method.')
 
     def __repr__(self):
         """

aggregate/distributions.py

@@ -2769,6 +2769,9 @@ def q(self, p, kind='lower'):
 
         return self._var_tvar_function[kind](p)
 
+    # for consistency with scipy
+    ppf = q
+
     def _make_var_tvar(self, ser):
         dict_ans = {}
         qf = make_var_tvar(ser)

aggregate/extensions/figures.py

@@ -9,7 +9,7 @@
 import matplotlib as mpl
 from .. import build, qd
 from .. constants import FIG_H, FIG_W, PLOT_FACE_COLOR
-from .. spectral import Distortion
+from .. spectral import Distortion, tvar_weights
 
 
 def adjusting_layer_losses():
@@ -366,4 +366,152 @@ def exact_cdf(x):
                                   ['p_total']]/a.bs
     df.index = [f'{x: 6.0f}' for x in df.index]
     df.index.name = 'x'
-    qd(df.iloc[:, [1,0,2,3,4, 5]], ff=lambda x: f'{x:11.3e}')
+    qd(df.iloc[:, [1,0,2,3,4, 5]], ff=lambda x: f'{x:11.3e}')
+
+
+def g_insurance_statistics(axi, dist, c='C0', ls='-', lw=1, diag=False, grid=False):
+    """
+    Six part plot with EL, premium, loss ratio, profit, layer ROE and P:S for g
+    axi = axis iterator with 6 axes
+    dist = distortion
+    Used to create PIR Figs 11.6 and 11.7
+    """
+    g = dist.g
+    N = 1000
+    ps = np.linspace(1 / (2 * N), 1, N, endpoint=False)
+    gs = g(ps)
+
+    dn = dist.name
+
+    # FIG: six panel display
+    for i, ys, key in zip(range(1, 7),
+                          [gs, ps / gs, gs / ps, gs - ps, (gs - ps) / (1 - ps), gs / (1 - gs)],
+                          ['Premium', 'Loss Ratio', 'Markup',
+                           'Margin', 'Discount Rate', 'Premium Leverage']):
+        a = next(axi)
+        if i == 1:
+            a.plot(ps, ys, ls=ls, c=c, lw=lw, label=dn)
+        else:
+            a.plot(ps, ys, ls=ls, lw=lw, c=c)
+        if i in [1] and diag:
+            a.plot(ps, ps, color='k', linewidth=0.25)
+        a.set(title=key)
+        if i == 3 or i == 6:
+            a.axis([0, 1, 0, 5])
+            a.set(aspect=1 / 5)
+        elif i == 5:
+            # discount
+            a.axis([0, 1, 0, .5])
+            a.set(aspect=1 / .5)
+        else:
+            a.axis([0, 1, 0, 1])
+            a.set(aspect=1)
+        if i == 1:
+            a.legend(loc='lower right')
+        if grid:
+            a.grid(lw=0.25)
+
+
+def g_risk_appetite(axi, dist, c='C0', ls='-', N=1000, lw=1, grid=False, xlabel=True, title=True, add_tvar=False):
+    """
+    Plot to illustrate the risk appetite associated with a distortion g.
+    Derived from ``g_insurance_statistics``.
+    Plots premium, loss ratio, margin, return (easier to understand than discount),
+    VaR wts and optionally TVaR wts
+    axi = axis iterator with 6 axes
+    dist = distortion
+    Used to create PIR Figs 11.6 and 11.7
+    """
+    g = dist.g
+    ps = np.linspace(1 / (2 * N), 1, N, endpoint=False)
+    gs = g(ps)
+
+    # var weight
+    gp = dist.g_prime(ps)
+
+    # tvar weight
+    wt_fun = tvar_weights(dist)
+    ps01 = np.linspace(0, 1, N+1)
+    tvar = wt_fun(ps01)
+
+    # labels etc.
+    dn = dist.name.replace(' ', '\n').replace('aCC', 'CC')
+    isccoc = dist.name.lower().find('ccoc') >= 0
+    istvar = dist.name.lower().find('tvar') >= 0
+
+    for i, ys, key in zip(range(6),
+                          [gs,
+                           ps / gs,
+                           gs - ps,
+                           (gs - ps) / (1 - gs),
+                           gp,
+                           tvar],
+                          ['Premium',
+                           'Loss ratio',
+                           'Margin',
+                           'Return on capital',
+                           'VaR weight',
+                           'TVaR p weight']):
+        if i == 5 and not add_tvar:
+            # skip tvar weights
+            continue
+        a = next(axi)
+        if key == 'VaR weight' and istvar:
+            ds = 'steps-post'
+        elif key == 'TVaR p weight' and (istvar or isccoc):
+            ds = 'steps-mid'
+        else:
+            ds = 'default'
+        kwargs = {'ls': ls, 'c': c, 'lw': lw, 'ds': ds}
+        if i == 0:
+            a.plot(ps, ys, label=dn, **kwargs)
+            a.legend(loc='lower right', fontsize=10)
+        elif i < 5:
+            a.plot(ps, ys, **kwargs)
+        else:
+            a.plot(ps01, ys, **kwargs)
+        if title:
+            a.set(title=key)
+        if i in (1, 3, 4):
+            mn, mx = a.get_ylim()
+            mx = max(1.025, min(5, mx * 1.1))
+            # a.set_ylim(0)
+            a.axis([-0.025, 1.025, -0.025, mx])
+            a.set(aspect=1 / mx)
+        elif i == 2:
+            a.axis([-0.025, 1.025, -0.025, .525])
+            a.set(aspect=2)
+        elif i in (0,1):
+            a.axis([-0.025, 1.025, -0.025, 1.025])
+            a.set(aspect='equal')
+        elif i == 5:
+            pass
+        else:
+            a.axis([-0.025, 1.025, -0.025, 1.025])
+            a.set(aspect=1)
+        if isccoc:
+            if key == 'Premium':
+                # add zero point
+                a.plot(0, 0, 'o', c=c)
+            if key == 'VaR weight':
+                # add var mass
+                mx = 2.2
+                line, = a.plot(0, mx, '*', c=c)  # Point above the plot area
+                # Allow plotting outside of the plot area
+                line.set_clip_on(False)
+            if key == 'Return on capital':
+                # add var mass
+                mx = a.get_ylim()[1] * 1.1
+                line, = a.plot(0, mx, '*', c=c)  # Point above the plot area
+                # Allow plotting outside of the plot area
+                line.set_clip_on(False)
+        if grid:
+            a.grid(lw=0.25)
+        if xlabel:
+            if i == 0:
+                a.set(xlabel='Exceedance probability\n(large losses on left)')
+            elif i == 5:
+                a.set(xlabel='p value\n(mean on left, max on right)')
+            else:
+                a.set(xlabel='Exceedance probability')
+    # print(np.sum(gp))

aggregate/extensions/risk_progression.py

@@ -146,9 +146,9 @@ def make_up_down(ser):
     u = np.maximum(0, dy).cumsum()
     d = -np.minimum(0, dy).cumsum()
     c = u - d
-    u.name = 'up'
-    d.name = 'down'
-    c.name = 'recreated'
+    u.name = 'Ins'
+    d.name = 'Fin'
+    c.name = 'Ins - Fin'
     return u, d, c
 
 
@@ -197,13 +197,14 @@ def plot_up_down(self, udd, axs):
 
     # left and middle plots
     for unit, ax, recreated_c in zip(self.unit_names, axs.flat, ['C0', 'C1']):
-        ax = self.density_df[f'exeqa_{unit}'].plot(ax=ax, lw=.5, c='C7', drawstyle='steps-mid')
+        ax = self.density_df[f'exeqa_{unit}'].plot(ax=ax, lw=.5, c='C7', drawstyle='steps-mid',
+                                                   label=f'E[{unit} | X]')
         (udd.up_functions[unit] - udd.down_functions[unit]
-         ).plot(ax=ax, lw=1.5, ls='-', c=recreated_c, label='recreated', drawstyle='steps-post')
+         ).plot(ax=ax, lw=1.5, ls='-', c=recreated_c, label='Ins - Fin', drawstyle='steps-post')
         udd.up_functions[unit].plot(ax=ax,   c='C3', drawstyle='steps-post', lw=1, ls='--')
         udd.down_functions[unit].plot(ax=ax, c='C5', drawstyle='steps-post', lw=1, ls='-.')
         ax.legend()
-        ax.set(xlabel='loss', ylabel='up or down function')
+        ax.set(xlabel='X, total', ylabel='Unit or conditional loss')
 
     # plot ud distributions (right hand plot)
     ax = axs.flat[-1]
@@ -241,7 +242,7 @@ def price_work(dn, series, names_ex):
     return bit
 
 
-def price_compare(self, dn, projection_dists, ud_dists):
+def price_compare(self, dn, projection_dists, ud_dists, allocation='linear'):
     """
     Build out pricing comparison waterfall
 
@@ -251,9 +252,9 @@ def price_compare(self, dn, projection_dists, ud_dists):
 
     # linear natural allocation pricing
     # KLUDGE
-    lna_pricea = self.price(self.q(1), dn, view='ask')
+    lna_pricea = self.price(self.q(1), dn, allocation=allocation, view='ask')
     # display(lna_pricea.df)
-    lna_priceb = self.price(self.q(1), dn, view='bid')
+    lna_priceb = self.price(self.q(1), dn, allocation=allocation, view='bid')
     na_price = lna_pricea.df[['L', 'P']]
     na_price.columns = ['el', 'ask']
     # if this is nan it gets dropped from stack?!
@@ -302,7 +303,7 @@ def price_compare(self, dn, projection_dists, ud_dists):
     return compare
 
 
-def full_monty(self, dn, truncate=True, smooth=16, plot=True):
+def full_monty(self, dn, truncate=True, smooth=16, plot=True, allocation='linear'):
     """
     One-stop shop for a Portfolio self
     Unlimited assets
@@ -342,10 +343,26 @@ def full_monty(self, dn, truncate=True, smooth=16, plot=True):
         axs1 = axs[3, :]
         plot_up_down(self, ud_dists, axs1)
 
-    compare = price_compare(self, dn, projection_dists, ud_dists)
+    compare = price_compare(self, dn, projection_dists, ud_dists, allocation=allocation)
     compare['umd'] = compare['up'] - compare['down']
-
-    RiskProgression = namedtuple('RiskProgression', ['compare_df', 'projection_dists', 'ud_dists'])
-    ans = RiskProgression(compare, projection_dists, ud_dists)
+    compare2 = compare.copy()
+    for l in compare2.index.levels[0]:
+        m = compare2.loc[(l, 'ask')] - compare2.loc[(l, 'el')]
+        compare2.loc[(l, 'margin'), :] = m
+    compare2 = compare2.sort_index()
+    compare2 = compare2.rename(columns={'lna': 'Linear NA' ,
+                      'sa': 'Standalone',
+                      'proj_sa': 'Projection SA',
+                      'up': 'Ins',
+                      'down': 'Fin',
+                      'umd': 'Ins - Fin'})
+    # or
+    # {'Linear NA': 'NA(Xi)', 'Standalone': 'ρ(Xi)',
+    #                  'Projection SA': 'ρ(E[Xi | X])',
+    #                  'Ins': 'ρ(Ins)', 'Fin': 'ρ(Fin)', 'Ins - Fin': 'ρ(Ins) - ρ(Fin)'
+
+    RiskProgression = namedtuple('RiskProgression',
+                                 ['compare_df', 'compare_df2', 'projection_dists', 'ud_dists'])
+    ans = RiskProgression(compare, compare2, projection_dists, ud_dists)
     return ans