diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index eccabac..dceadc1 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -42,7 +42,7 @@ repos:
       - id: python-use-type-annotations
       - id: text-unicode-replacement-char
   - repo: https://github.com/pycqa/isort
-    rev: 8.0.1
+    rev: 9.0.0b1
     hooks:
       - id: isort
         name: isort
@@ -55,13 +55,13 @@ repos:
   #       args:
   #         - --py37-plus
   - repo: https://github.com/psf/black-pre-commit-mirror
-    rev: 26.1.0
+    rev: 26.5.1
     hooks:
       - id: black
         language_version: python3.12
         exclude: tests/utils/fast_upper_envelope_org.py
   - repo: https://github.com/astral-sh/ruff-pre-commit
-    rev: v0.15.4
+    rev: v0.16.1
     hooks:
       - id: ruff
         # exclude: |
@@ -70,7 +70,7 @@ repos:
         #     docs/source/conf.py|
         #   )$
   - repo: https://github.com/PyCQA/docformatter
-    rev: v1.7.7
+    rev: v1.7.8
     hooks:
       - id: docformatter
         args:
diff --git a/docs/time_period2_ops.py b/docs/time_period2_ops.py
index 4242d57..45ff026 100644
--- a/docs/time_period2_ops.py
+++ b/docs/time_period2_ops.py
@@ -24,7 +24,7 @@ def _parse_args() -> argparse.Namespace:
 
 
 def utility_crra_jax(
-    consumption: jnp.ndarray, choice: int, params: Dict[str, float]
+    consumption: jnp.ndarray, choice: int, params: dict[str, float]
 ) -> jnp.ndarray:
     utility_consumption = (consumption ** (1 - params["rho"]) - 1) / (1 - params["rho"])
     utility = utility_consumption - (1 - choice) * params["delta"]
@@ -50,7 +50,7 @@ def value_func_numba(
     test_resources / f"pol{period}.csv", delimiter=",", dtype=float
 )
 
-params: Dict[str, float] = {"beta": 0.95, "rho": 1.95, "delta": 0.35}
+params: dict[str, float] = {"beta": 0.95, "rho": 1.95, "delta": 0.35}
 state_choice = {"lagged_choice": 0, "choice": 0}
 
 
diff --git a/docs/tutorials/getting_started.ipynb b/docs/tutorials/getting_started.ipynb
index f343212..cf0e55e 100644
--- a/docs/tutorials/getting_started.ipynb
+++ b/docs/tutorials/getting_started.ipynb
@@ -2,25 +2,35 @@
  "cells": [
   {
    "cell_type": "code",
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "from upper_envelope.fues_numba.fues_numba import fast_upper_envelope_wrapper\n",
-    "import numba as nb\n",
-    "from collections import namedtuple\n"
-   ],
+   "execution_count": 1,
+   "id": "c71bb4b54fd1da58",
    "metadata": {
-    "collapsed": false,
     "ExecuteTime": {
      "end_time": "2024-05-24T06:42:04.589484405Z",
      "start_time": "2024-05-24T06:42:04.167227740Z"
-    }
+    },
+    "collapsed": false
    },
-   "id": "c71bb4b54fd1da58",
-   "execution_count": 1
+   "outputs": [],
+   "source": [
+    "from collections import namedtuple\n",
+    "\n",
+    "import numba as nb\n",
+    "import numpy as np\n",
+    "from upper_envelope.fues_numba.fues_numba import fast_upper_envelope_wrapper\n"
+   ]
   },
   {
    "cell_type": "code",
+   "execution_count": 2,
+   "id": "ab4b0dcb970dac41",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2024-05-24T06:42:04.611236211Z",
+     "start_time": "2024-05-24T06:42:04.609614665Z"
+    },
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "@nb.njit\n",
@@ -50,27 +60,18 @@
     "    utility = utility_consumption - (1 - params_ntuple.choice) * params_ntuple.delta\n",
     "\n",
     "    return utility"
-   ],
-   "metadata": {
-    "collapsed": false,
-    "ExecuteTime": {
-     "end_time": "2024-05-24T06:42:04.611236211Z",
-     "start_time": "2024-05-24T06:42:04.609614665Z"
-    }
-   },
-   "id": "ab4b0dcb970dac41",
-   "execution_count": 2
+   ]
   },
   {
    "cell_type": "code",
    "execution_count": 3,
    "id": "initial_id",
    "metadata": {
-    "collapsed": true,
     "ExecuteTime": {
      "end_time": "2024-05-24T06:42:04.613370376Z",
      "start_time": "2024-05-24T06:42:04.609954700Z"
-    }
+    },
+    "collapsed": true
    },
    "outputs": [],
    "source": [
@@ -89,6 +90,15 @@
   },
   {
    "cell_type": "code",
+   "execution_count": 4,
+   "id": "61b7b971c6f81237",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2024-05-24T06:42:04.614201145Z",
+     "start_time": "2024-05-24T06:42:04.610074325Z"
+    },
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "resource_dir = \"../../tests/resources/\"\n",
@@ -108,19 +118,19 @@
     "    \"n_constrained_points_to_add\": n_constrained_points_to_add,\n",
     "    \"n_points_to_scan\": 10,\n",
     "}"
-   ],
-   "metadata": {
-    "collapsed": false,
-    "ExecuteTime": {
-     "end_time": "2024-05-24T06:42:04.614201145Z",
-     "start_time": "2024-05-24T06:42:04.610074325Z"
-    }
-   },
-   "id": "61b7b971c6f81237",
-   "execution_count": 4
+   ]
   },
   {
    "cell_type": "code",
+   "execution_count": 5,
+   "id": "415a872b98d65631",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2024-05-24T06:42:04.614607376Z",
+     "start_time": "2024-05-24T06:42:04.610206856Z"
+    },
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "\n",
@@ -130,19 +140,19 @@
     "tuning_params_tuple = namedtuple(\"tunings\", tuning_params.keys())(\n",
     "    *tuning_params.values()\n",
     ")"
-   ],
-   "metadata": {
-    "collapsed": false,
-    "ExecuteTime": {
-     "end_time": "2024-05-24T06:42:04.614607376Z",
-     "start_time": "2024-05-24T06:42:04.610206856Z"
-    }
-   },
-   "id": "415a872b98d65631",
-   "execution_count": 5
+   ]
   },
   {
    "cell_type": "code",
+   "execution_count": 6,
+   "id": "df76ba014c57934d",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2024-05-24T06:42:14.783923576Z",
+     "start_time": "2024-05-24T06:42:04.611563430Z"
+    },
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "endog_grid_refined, policy_refined, value_refined = fast_upper_envelope_wrapper(\n",
@@ -156,16 +166,7 @@
     "    discount_factor=beta,\n",
     "    tuning_params=tuning_params_tuple,\n",
     ")"
-   ],
-   "metadata": {
-    "collapsed": false,
-    "ExecuteTime": {
-     "end_time": "2024-05-24T06:42:14.783923576Z",
-     "start_time": "2024-05-24T06:42:04.611563430Z"
-    }
-   },
-   "id": "df76ba014c57934d",
-   "execution_count": 6
+   ]
   }
  ],
  "metadata": {
diff --git a/docs/tutorials/ue_drued_jorg.ipynb b/docs/tutorials/ue_drued_jorg.ipynb
index ec162bd..fa21e89 100644
--- a/docs/tutorials/ue_drued_jorg.ipynb
+++ b/docs/tutorials/ue_drued_jorg.ipynb
@@ -26,10 +26,10 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "import numpy as np\n",
     "import jax\n",
     "import jax.numpy as jnp\n",
     "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
     "\n",
     "import upper_envelope.jax as upenv\n",
     "\n",
diff --git a/src/upper_envelope/jax/drued_jorg_jax.py b/src/upper_envelope/jax/drued_jorg_jax.py
index 6b682c6..f32d703 100644
--- a/src/upper_envelope/jax/drued_jorg_jax.py
+++ b/src/upper_envelope/jax/drued_jorg_jax.py
@@ -1,7 +1,8 @@
 from __future__ import annotations
 
+from collections.abc import Callable
 from functools import partial
-from typing import Callable, Dict, Optional
+from typing import Dict, Optional
 
 import jax
 import jax.numpy as jnp
@@ -16,7 +17,7 @@ def drued_jorg_jax(
     expected_value_zero_savings: jnp.ndarray | float,
     value_function: Callable,
     value_function_args=(),
-    value_function_kwargs: Optional[Dict] = None,
+    value_function_kwargs: dict | None = None,
 ):
     """Compute a simple 1D upper envelope on a given common grid.
 
diff --git a/src/upper_envelope/jax/fues_jax/check_and_scan_funcs.py b/src/upper_envelope/jax/fues_jax/check_and_scan_funcs.py
index 77fc653..20e8367 100644
--- a/src/upper_envelope/jax/fues_jax/check_and_scan_funcs.py
+++ b/src/upper_envelope/jax/fues_jax/check_and_scan_funcs.py
@@ -256,7 +256,7 @@ def forward_scan(
     n_points_to_scan: int,
     is_scan_needed,
     jump_thresh: float,
-) -> Tuple[float, int]:
+) -> tuple[float, int]:
     """Find next point on same value function as most recent point on upper envelope.
 
     We use the forward scan to find the next point that lies on the same value
@@ -322,7 +322,7 @@ def backward_scan(
     n_points_to_scan: int,
     is_scan_needed,
     jump_thresh: float,
-) -> Tuple[float, int]:
+) -> tuple[float, int]:
     """Find previous point on same value function as idx_to_scan_from.
 
     We use the backward scan to find the preceding point that lies on the same value
diff --git a/src/upper_envelope/jax/fues_jax/fues_jax.py b/src/upper_envelope/jax/fues_jax/fues_jax.py
index 822464b..51ab049 100644
--- a/src/upper_envelope/jax/fues_jax/fues_jax.py
+++ b/src/upper_envelope/jax/fues_jax/fues_jax.py
@@ -6,8 +6,9 @@
 
 """
 
+from collections.abc import Callable
 from functools import partial
-from typing import Callable, Dict, Optional, Tuple
+from typing import Dict, Optional, Tuple
 
 import jax
 import jax.numpy as jnp
@@ -35,13 +36,13 @@ def fues_jax(
     value: jnp.ndarray,
     expected_value_zero_savings: jnp.ndarray | float,
     value_function: Callable,
-    value_function_args: Optional[Tuple] = (),
-    value_function_kwargs: Optional[Dict] = None,
+    value_function_args: tuple | None = (),
+    value_function_kwargs: dict | None = None,
     n_constrained_points_to_add=None,
     n_final_wealth_grid=None,
     jump_thresh=2,
     n_points_to_scan=10,
-) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
+) -> tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
     """Drop suboptimal points and refines the endogenous grid, policy, and value.
 
     Computes the upper envelope over the overlapping segments of the
@@ -185,7 +186,7 @@ def fues_jax_unconstrained(
     n_final_wealth_grid=None,
     jump_thresh=2,
     n_points_to_scan=10,
-) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
+) -> tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
     """Remove suboptimal points from the endogenous grid, policy, and value function.
 
     Args:
@@ -249,8 +250,8 @@ def scan_value_function(
     expected_value_zero_savings,
     n_final_wealth_grid: int,
     jump_thresh: float,
-    n_points_to_scan: Optional[int] = 0,
-) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
+    n_points_to_scan: int | None = 0,
+) -> tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
     """Scan the value function to remove suboptimal points and add intersection points.
 
     Args:
diff --git a/src/upper_envelope/math_funcs.py b/src/upper_envelope/math_funcs.py
index e13dc6c..9beb680 100644
--- a/src/upper_envelope/math_funcs.py
+++ b/src/upper_envelope/math_funcs.py
@@ -158,7 +158,7 @@ def _find_linear_intersection(
     y3: float | jnp.ndarray,
     x4: float | jnp.ndarray,
     y4: float | jnp.ndarray,
-) -> Tuple[float | jnp.ndarray, float | jnp.ndarray]:
+) -> tuple[float | jnp.ndarray, float | jnp.ndarray]:
     """Find the linear intersection of two lines.
 
     Args:
@@ -176,7 +176,6 @@ def _find_linear_intersection(
         tuple: x and y coordinates of the intersection point.
 
     """
-
     slope1 = calc_gradient(x1, y1, x2, y2)
     slope2 = calc_gradient(x3, y3, x4, y4)
 
diff --git a/src/upper_envelope/numba/drued_jorg_numba.py b/src/upper_envelope/numba/drued_jorg_numba.py
index 172d3f9..ffa5903 100644
--- a/src/upper_envelope/numba/drued_jorg_numba.py
+++ b/src/upper_envelope/numba/drued_jorg_numba.py
@@ -1,4 +1,4 @@
-from typing import Callable
+from collections.abc import Callable
 
 import numpy as np
 from numba import njit
diff --git a/src/upper_envelope/numba/fues_numba/fues_numba.py b/src/upper_envelope/numba/fues_numba/fues_numba.py
index 7a0ed91..49c7c71 100644
--- a/src/upper_envelope/numba/fues_numba/fues_numba.py
+++ b/src/upper_envelope/numba/fues_numba/fues_numba.py
@@ -6,7 +6,8 @@
 
 """
 
-from typing import Callable, Optional, Tuple
+from collections.abc import Callable
+from typing import Optional, Tuple
 
 import numpy as np
 from numba import njit
@@ -19,12 +20,12 @@ def fues_numba(
     value: np.ndarray,
     expected_value_zero_savings: np.ndarray | float,
     value_function: Callable,
-    value_function_args: Tuple,
+    value_function_args: tuple,
     n_constrained_points_to_add=None,
     n_final_wealth_grid=None,
     jump_thresh=2,
     n_points_to_scan=10,
-) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
     """Drop suboptimal points and refine the endogenous grid, policy, and value.
 
     Computes the upper envelope over the overlapping segments of the
@@ -146,7 +147,7 @@ def fues_numba_unconstrained(
     policy: np.ndarray,
     jump_thresh=2,
     n_points_to_scan=10,
-) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
     """Remove suboptimal points from the endogenous grid, policy, and value function.
 
     Args:
@@ -170,7 +171,6 @@ def fues_numba_unconstrained(
             containing refined value function.
 
     """
-
     endog_grid = endog_grid[np.where(~np.isnan(value))[0]]
     policy = policy[np.where(~np.isnan(value))]
     value = value[np.where(~np.isnan(value))]
@@ -209,9 +209,9 @@ def scan_value_function(
     value: np.ndarray,
     policy: np.ndarray,
     exog_grid: np.ndarray,
-    jump_thresh: Optional[float] = 2,
-    n_points_to_scan: Optional[int] = 0,
-) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+    jump_thresh: float | None = 2,
+    n_points_to_scan: int | None = 0,
+) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
     """Scan the value function to remove suboptimal points and add intersection points.
 
     Args:
@@ -234,7 +234,6 @@ def scan_value_function(
             the optimal points are kept.
 
     """
-
     value_refined, policy_refined, endog_grid_refined = _initialize_refined_arrays(
         value, policy, endog_grid
     )
@@ -524,7 +523,7 @@ def _forward_scan(
     idx_current: int,
     idx_next: int,
     n_points_to_scan: int,
-) -> Tuple[float, int, int]:
+) -> tuple[float, int, int]:
     """Scan forward to check whether next point is optimal.
 
     Args:
@@ -550,7 +549,6 @@ def _forward_scan(
             the same value function.
 
     """
-
     is_next_on_same_value = 0
     idx_on_same_value = 0
     grad_next_on_same_value = 0
@@ -599,7 +597,7 @@ def _backward_scan(
     jump_thresh: float,
     idx_current: int,
     idx_next: int,
-) -> Tuple[float, int]:
+) -> tuple[float, int]:
     """Scan backward to check whether current point is optimal.
 
     Args:
@@ -623,7 +621,6 @@ def _backward_scan(
             previous point on the same value function.
 
     """
-
     is_before_on_same_value = 0
     sub_idx_point_before_on_same_value = 0
     grad_before_on_same_value = 0
@@ -695,7 +692,7 @@ def _linear_intersection(
     y3: float | np.ndarray,
     x4: float | np.ndarray,
     y4: float | np.ndarray,
-) -> Tuple[float, float]:
+) -> tuple[float, float]:
     """Find the intersection of two lines.
 
     Args:
@@ -713,7 +710,6 @@ def _linear_intersection(
         tuple: x and y coordinates of the intersection point.
 
     """
-
     slope1 = (y2 - y1) / (x2 - x1)
     slope2 = (y4 - y3) / (x4 - x3)
 
@@ -741,8 +737,8 @@ def _augment_grids(
     min_wealth_grid: float,
     n_constrained_points_to_add: int,
     value_function: Callable,
-    value_function_args: Tuple,
-) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+    value_function_args: tuple,
+) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
     """Extends the endogenous wealth grid, value, and policy functions to the left.
 
     Args:
@@ -796,7 +792,7 @@ def _augment_grids(
 @njit
 def _initialize_refined_arrays(
     value: np.ndarray, policy: np.ndarray, endog_grid: np.ndarray
-) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
     value_refined = np.empty_like(value)
     policy_refined = np.empty_like(policy)
     endog_grid_refined = np.empty_like(endog_grid)
diff --git a/tests/conftest.py b/tests/conftest.py
index b258f2d..bea943f 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -16,15 +16,15 @@
 sys.path.append(os.path.join(os.path.dirname(__file__), "utils"))
 
 
-def pytest_sessionstart(session):  # noqa: ARG001
+def pytest_sessionstart(session):
     jax.config.update("jax_enable_x64", val=True)
 
 
-def pytest_configure(config):  # noqa: ARG001
+def pytest_configure(config):
     """Called after command line options have been parsed."""
     os.environ["NUMBA_DISABLE_JIT"] = "1"
 
 
-def pytest_unconfigure(config):  # noqa: ARG001
+def pytest_unconfigure(config):
     """Called before test process is exited."""
     os.environ.pop("NUMBA_DISABLE_JIT", None)
diff --git a/tests/test_drued_jorg_numba.py b/tests/test_drued_jorg_numba.py
index 4b061e9..d56cc55 100644
--- a/tests/test_drued_jorg_numba.py
+++ b/tests/test_drued_jorg_numba.py
@@ -1,10 +1,9 @@
 """Tests for `drued_jorg_numba`.
 
-This test mirrors `tests/test_jorg_drued_jax.py` but exercises the numba
-implementation.
+This test mirrors `tests/test_jorg_drued_jax.py` but exercises the numba implementation.
 
-We compare against `upenv.fues_jax`, but only on evaluation points that lie on
-reference line segments that are not affected by explicit intersection handling.
+We compare against `upenv.fues_jax`, but only on evaluation points that lie on reference
+line segments that are not affected by explicit intersection handling.
 
 """
 
@@ -26,7 +25,7 @@
 
 
 def utility_crra(
-    consumption: jnp.ndarray, choice: int, params: Dict[str, float]
+    consumption: jnp.ndarray, choice: int, params: dict[str, float]
 ) -> jnp.ndarray:
     utility_consumption = (consumption ** (1 - params["rho"]) - 1) / (1 - params["rho"])
     utility = utility_consumption - (1 - choice) * params["delta"]
diff --git a/tests/test_fues_jax.py b/tests/test_fues_jax.py
index 03f9108..f84575e 100644
--- a/tests/test_fues_jax.py
+++ b/tests/test_fues_jax.py
@@ -33,7 +33,7 @@
 def utility_crra(
     consumption: jnp.array,
     choice: int,
-    params: Dict[str, float],
+    params: dict[str, float],
 ) -> jnp.array:
     """Computes the agent's current utility based on a CRRA utility function.
 
diff --git a/tests/test_jorg_drued_jax.py b/tests/test_jorg_drued_jax.py
index 0f88c60..801e21e 100644
--- a/tests/test_jorg_drued_jax.py
+++ b/tests/test_jorg_drued_jax.py
@@ -33,7 +33,7 @@
 
 
 def utility_crra(
-    consumption: jnp.ndarray, choice: int, params: Dict[str, float]
+    consumption: jnp.ndarray, choice: int, params: dict[str, float]
 ) -> jnp.ndarray:
     utility_consumption = (consumption ** (1 - params["rho"]) - 1) / (1 - params["rho"])
     utility = utility_consumption - (1 - choice) * params["delta"]
diff --git a/tests/utils/fast_upper_envelope_org.py b/tests/utils/fast_upper_envelope_org.py
index 6db12ad..1da4149 100644
--- a/tests/utils/fast_upper_envelope_org.py
+++ b/tests/utils/fast_upper_envelope_org.py
@@ -5,7 +5,8 @@
 https://dx.doi.org/10.2139/ssrn.4181302
 
 """
-from typing import Callable, Optional, Tuple
+from collections.abc import Callable
+from typing import Optional, Tuple
 
 import numpy as np
 
@@ -17,7 +18,7 @@ def fast_upper_envelope_wrapper_org(
     exog_grid: np.ndarray,
     choice: int,  # noqa: U100
     compute_utility: Callable,  # noqa: U100
-) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
     """Drop suboptimal points and refine the endogenous grid, policy, and value.
 
     Computes the upper envelope over the overlapping segments of the
@@ -95,9 +96,9 @@ def fast_upper_envelope(
     value: np.ndarray,
     policy: np.ndarray,
     exog_grid: np.ndarray,
-    jump_thresh: Optional[float] = 2,
-    b: Optional[float] = 1e-10,
-) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+    jump_thresh: float | None = 2,
+    b: float | None = 1e-10,
+) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
     """Remove suboptimal points from the endogenous grid, policy, and value function.
 
     Args:
@@ -289,7 +290,7 @@ def _scan_org(e_grid, vf, c, a_prime, m_bar, lb, fwd_scan_do=True):  # noqa: U10
                     j = np.copy(np.array([i]))[0] + 1
 
                 else:
-                    previous_opt_is_intersect = False  # noqa: F841
+                    previous_opt_is_intersect = False
                     if g_1 > g_j_minus_1:
                         previous_opt_is_intersect = True  # noqa: F841
 
diff --git a/tests/utils/interpolation.py b/tests/utils/interpolation.py
index 4cfdbcb..c7c03c8 100644
--- a/tests/utils/interpolation.py
+++ b/tests/utils/interpolation.py
@@ -141,7 +141,7 @@ def linear_interpolation_formula(
 
 def get_index_high_and_low(
     x: np.ndarray, x_new: np.ndarray | float
-) -> Tuple[np.ndarray, np.ndarray]:
+) -> tuple[np.ndarray, np.ndarray]:
     """Get index of the highest value in x that is smaller than x_new.
 
     Args:
diff --git a/tests/utils/upper_envelope_fedor.py b/tests/utils/upper_envelope_fedor.py
index 9895e76..e78532f 100644
--- a/tests/utils/upper_envelope_fedor.py
+++ b/tests/utils/upper_envelope_fedor.py
@@ -5,7 +5,8 @@
 
 """
 
-from typing import Callable, Dict, List, Tuple
+from collections.abc import Callable
+from typing import Dict, List, Tuple
 
 import numpy as np
 from scipy.optimize import brenth as root
@@ -17,10 +18,10 @@ def upper_envelope(
     policy: np.ndarray,
     value: np.ndarray,
     exog_grid: np.ndarray,
-    state_choice_vec: Dict,
-    params: Dict[str, float],
+    state_choice_vec: dict,
+    params: dict[str, float],
     compute_utility: Callable,
-) -> Tuple[np.ndarray, np.ndarray]:
+) -> tuple[np.ndarray, np.ndarray]:
     """Runs the Upper Envelope algorithm and drops sub-optimal points.
     Calculates the upper envelope over the overlapping segments of the
     decision-specific value functions, which in fact are value "correspondences"
@@ -133,7 +134,7 @@ def upper_envelope(
 
 def locate_non_concave_regions(
     value: np.ndarray,
-) -> List[np.ndarray]:
+) -> list[np.ndarray]:
     """Locates non-concave regions.
     Find non-monotonicity in the endogenous wealth grid where a grid point
     to the right is smaller than its preceding point. Put differently, the
@@ -200,8 +201,8 @@ def locate_non_concave_regions(
 
 
 def compute_upper_envelope(
-    segments: List[np.ndarray],
-) -> Tuple[np.ndarray, np.ndarray]:
+    segments: list[np.ndarray],
+) -> tuple[np.ndarray, np.ndarray]:
     """Compute upper envelope and refines value function correspondence.
     The upper envelope algorithm detects suboptimal points in the value function
     correspondence. Consequently, (i) the suboptimal points are removed and the
@@ -531,7 +532,7 @@ def _augment_grid(
     n_grid_wealth: int,
     params,
     compute_utility: Callable,
-) -> Tuple[np.ndarray, np.ndarray]:
+) -> tuple[np.ndarray, np.ndarray]:
     """Extends the endogenous wealth grid, value, and policy function to the left.
 
     Args:
@@ -563,7 +564,6 @@ def _augment_grid(
             Shape (2, *n_grid_augmented*).
 
     """
-
     grid_points_to_add = np.linspace(min_wealth_grid, value[0, 1], n_grid_wealth // 10)[
         :-1
     ]
@@ -593,7 +593,7 @@ def _augment_grid(
 
 def _partition_grid(
     value_correspondence: np.ndarray, j: int
-) -> Tuple[np.ndarray, np.ndarray]:
+) -> tuple[np.ndarray, np.ndarray]:
     """Splits the grid into two parts, 1,..., j and j, j+1,..., J.
 
     Note that the index ``j``, after which the separation occurs,