diff --git a/.github/workflows/bump.yml b/.github/workflows/bump.yml
index c4dd317b..541d276d 100644
--- a/.github/workflows/bump.yml
+++ b/.github/workflows/bump.yml
@@ -11,20 +11,20 @@ jobs:
     runs-on: ubuntu-latest
     if: ${{ contains(github.ref, 'release/') }}
     steps:
-    - uses: actions/checkout@v2
-    - uses: actions/setup-python@v2
-    - name: Install poetry
-      run: pip install poetry
-    - name: Bump version
-      run: git branch --show-current | sed 's|release/||' | xargs poetry version | { printf '::set-output name=PR_TITLE::'; cat; }
-      id: bump
-    - name: Bump version 2
-      run:  git branch --show-current | sed 's|release/||' | xargs -I {} echo '__version__ = "{}"' > pams/version.py
-    - name: Create pull request
-      uses: peter-evans/create-pull-request@v3
-      with:
-        author: GitHub Actions <action@github.com>
-        commit-message: ${{ steps.bump.outputs.PR_TITLE }}
-        delete-branch: true
-        branch-suffix: short-commit-hash
-        title: ${{ steps.bump.outputs.PR_TITLE }}
+      - uses: actions/checkout@v2
+      - uses: actions/setup-python@v2
+      - name: Install poetry
+        run: pip install poetry
+      - name: Bump version
+        run: git branch --show-current | sed 's|release/||' | xargs poetry version | { printf '::set-output name=PR_TITLE::'; cat; }
+        id: bump
+      - name: Bump version 2
+        run: git branch --show-current | sed 's|release/||' | xargs -I {} echo '__version__ = "{}"' > pams/version.py
+      - name: Create pull request
+        uses: peter-evans/create-pull-request@v3
+        with:
+          author: GitHub Actions <action@github.com>
+          commit-message: ${{ steps.bump.outputs.PR_TITLE }}
+          delete-branch: true
+          branch-suffix: short-commit-hash
+          title: ${{ steps.bump.outputs.PR_TITLE }}
diff --git a/.github/workflows/ci-python-min.yml b/.github/workflows/ci-python-min.yml
index afb3a9a6..b426f84f 100644
--- a/.github/workflows/ci-python-min.yml
+++ b/.github/workflows/ci-python-min.yml
@@ -6,9 +6,9 @@ name: CI-min
 on:
   # Triggers the workflow on push or pull request events but only for the main branch
   push:
-    branches: [ dev, release/* ]
+    branches: [dev, release/*]
   pull_request:
-    branches: [ dev, release/* ]
+    branches: [dev, release/*]
 
   # Allows you to run this workflow manually from the Actions tab
   workflow_dispatch:
@@ -18,12 +18,12 @@ jobs:
   # This workflow contains a single job called "build"
   build:
     # The type of runner that the job will run on
-    runs-on:  ${{ matrix.platform }}
+    runs-on: ${{ matrix.platform }}
     strategy:
       max-parallel: 5
       matrix:
         platform: [ubuntu-latest]
-        python-version: [3.9]
+        python-version: [3.11]
 
     # Steps represent a sequence of tasks that will be executed as part of the job
     steps:
diff --git a/.github/workflows/ci-python-notebooks.yml b/.github/workflows/ci-python-notebooks.yml
index f2b5ca26..b1f0b1ae 100644
--- a/.github/workflows/ci-python-notebooks.yml
+++ b/.github/workflows/ci-python-notebooks.yml
@@ -6,9 +6,9 @@ name: CI-notebooks
 on:
   # Triggers the workflow on push or pull request events but only for the main branch
   push:
-    branches: [ main, dev, release/* ]
+    branches: [main, dev, release/*]
   pull_request:
-    branches: [ main, dev, release/* ]
+    branches: [main, dev, release/*]
 
   # Allows you to run this workflow manually from the Actions tab
   workflow_dispatch:
@@ -18,12 +18,12 @@ jobs:
   # This workflow contains a single job called "build"
   build:
     # The type of runner that the job will run on
-    runs-on:  ${{ matrix.platform }}
+    runs-on: ${{ matrix.platform }}
     strategy:
       max-parallel: 5
       matrix:
         platform: [ubuntu-latest]
-        python-version: [3.8]
+        python-version: [3.11]
 
     # Steps represent a sequence of tasks that will be executed as part of the job
     steps:
diff --git a/.github/workflows/ci-python.yml b/.github/workflows/ci-python.yml
index bc8dfcfa..1f831400 100644
--- a/.github/workflows/ci-python.yml
+++ b/.github/workflows/ci-python.yml
@@ -6,9 +6,9 @@ name: CI
 on:
   # Triggers the workflow on push or pull request events but only for the main branch
   push:
-    branches: [ main ]
+    branches: [main]
   pull_request:
-    branches: [ main ]
+    branches: [main]
 
   # Allows you to run this workflow manually from the Actions tab
   workflow_dispatch:
@@ -18,7 +18,7 @@ jobs:
   # This workflow contains a single job called "build"
   build:
     # The type of runner that the job will run on
-    runs-on:  ${{ matrix.platform }}
+    runs-on: ${{ matrix.platform }}
     strategy:
       max-parallel: 5
       matrix:
@@ -47,4 +47,4 @@ jobs:
       - name: Doc Test
         if: matrix.platform == 'ubuntu-latest'
         run: |
-          poetry run pytest --doctest-modules pams          
+          poetry run pytest --doctest-modules pams
diff --git a/.github/workflows/codecov.yml b/.github/workflows/codecov.yml
index 18baae52..2c1bd3de 100644
--- a/.github/workflows/codecov.yml
+++ b/.github/workflows/codecov.yml
@@ -6,9 +6,9 @@ name: codecov CI
 on:
   # Triggers the workflow on push or pull request events but only for the main branch
   push:
-    branches: [ main, dev, release/* ]
+    branches: [main, dev, release/*]
   pull_request:
-    branches: [ main ]
+    branches: [main]
 
   # Allows you to run this workflow manually from the Actions tab
   workflow_dispatch:
@@ -21,26 +21,26 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: [3.9]
+        python-version: [3.11]
 
     # Steps represent a sequence of tasks that will be executed as part of the job
     steps:
-    - uses: actions/checkout@v2
-    - name: Set up Python ${{ matrix.python-version }}
-      uses: actions/setup-python@v2.2.2
-      with:
-        python-version: ${{ matrix.python-version }}
-    - name: Install dependencies
-      run: |
-        python -m pip install --upgrade pip setuptools wheel
-        python -m pip install poetry
-        poetry install
-    - name: make cov report
-      run: |
-        poetry run pytest --cov=./ --cov-report=xml
-    - uses: codecov/codecov-action@v2
-      with:
-        token: ${{ secrets.CODECOV_TOKEN }} # not required for public repos
-        files: ./coverage.xml
-        flags: pytest
-        verbose: true
+      - uses: actions/checkout@v2
+      - name: Set up Python ${{ matrix.python-version }}
+        uses: actions/setup-python@v2.2.2
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Install dependencies
+        run: |
+          python -m pip install --upgrade pip setuptools wheel
+          python -m pip install poetry
+          poetry install
+      - name: make cov report
+        run: |
+          poetry run pytest --cov=./ --cov-report=xml
+      - uses: codecov/codecov-action@v2
+        with:
+          token: ${{ secrets.CODECOV_TOKEN }} # not required for public repos
+          files: ./coverage.xml
+          flags: pytest
+          verbose: true
diff --git a/.github/workflows/doc.yml b/.github/workflows/doc.yml
index 57889af4..cc4cd646 100644
--- a/.github/workflows/doc.yml
+++ b/.github/workflows/doc.yml
@@ -8,12 +8,12 @@ on:
 
 jobs:
   doc:
-    runs-on:  ${{ matrix.platform }}
+    runs-on: ${{ matrix.platform }}
     strategy:
       max-parallel: 5
       matrix:
         platform: [ubuntu-latest]
-        python-version: [3.9]
+        python-version: [3.11]
     steps:
       - uses: actions/checkout@v2
       - name: Set up Python ${{ matrix.python-version }}
diff --git a/.github/workflows/release.yml b/.github/workflows/release.yml
index 37cd92c3..ee221981 100644
--- a/.github/workflows/release.yml
+++ b/.github/workflows/release.yml
@@ -1,36 +1,36 @@
 name: Release
 on:
- pull_request:
-   branches:
-     - main
-   types:
-     - closed
+  pull_request:
+    branches:
+      - main
+    types:
+      - closed
 jobs:
   tagging:
     runs-on: ubuntu-latest
     if: github.event.pull_request.merged == true && startsWith(github.event.pull_request.head.ref, 'release/')
     steps:
-       - name: Get the version
-         id: get_version
-         run: |
-           echo ::set-output name=TAG::`echo $SOURCE_VERSION | cut -d / -f 2`
-         env:
-           SOURCE_VERSION: ${{ github.event.pull_request.head.ref }}
-       - name: Echo tag
-         run: echo ${{ steps.get_version.outputs.TAG }}
-       - uses: actions/checkout@v2
-       - run: |
-           git config --global user.email "masa.hirano.1996@gmail.com"
-           git config --global user.name "Masanori HIRANO"
-           git fetch origin ${{ github.event.pull_request.head.ref }}
-           git checkout main
-           git tag -a `echo '${{ github.event.pull_request.head.ref }}' | sed 's/release\///'` -m " "
-           git push origin `echo '${{ github.event.pull_request.head.ref }}' | sed 's/release\///'`
+      - name: Get the version
+        id: get_version
+        run: |
+          echo ::set-output name=TAG::`echo $SOURCE_VERSION | cut -d / -f 2`
+        env:
+          SOURCE_VERSION: ${{ github.event.pull_request.head.ref }}
+      - name: Echo tag
+        run: echo ${{ steps.get_version.outputs.TAG }}
+      - uses: actions/checkout@v2
+      - run: |
+          git config --global user.email "masa.hirano.1996@gmail.com"
+          git config --global user.name "Masanori HIRANO"
+          git fetch origin ${{ github.event.pull_request.head.ref }}
+          git checkout main
+          git tag -a `echo '${{ github.event.pull_request.head.ref }}' | sed 's/release\///'` -m " "
+          git push origin `echo '${{ github.event.pull_request.head.ref }}' | sed 's/release\///'`
 
   test:
     # The type of runner that the job will run on
     name: final test
-    runs-on:  ${{ matrix.platform }}
+    runs-on: ${{ matrix.platform }}
     needs: tagging
     strategy:
       max-parallel: 5
@@ -57,7 +57,7 @@ jobs:
           poetry run pflake8 .
           poetry run mypy .
           poetry run pytest tests/
-  
+
   releasetest:
     # The type of runner that the job will run on
     name: release test
@@ -65,32 +65,32 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: [3.9]
+        python-version: [3.11]
 
     # Steps represent a sequence of tasks that will be executed as part of the job
     steps:
-    - uses: actions/checkout@v2
-    - name: Set up Python ${{ matrix.python-version }}
-      uses: actions/setup-python@v2.2.2
-      with:
-        python-version: ${{ matrix.python-version }}
-    - name: Install dependencies
-      run: |
-        python -m pip install --upgrade pip setuptools wheel
-        python -m pip install poetry
-        poetry install
-    - name: test release
-      run: |
-        poetry config repositories.testpypi https://test.pypi.org/legacy/
-        poetry publish --build -r testpypi --username __token__ --password ${{ secrets.TEST_PYPI_TOKEN }}
-  
+      - uses: actions/checkout@v2
+      - name: Set up Python ${{ matrix.python-version }}
+        uses: actions/setup-python@v2.2.2
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Install dependencies
+        run: |
+          python -m pip install --upgrade pip setuptools wheel
+          python -m pip install poetry
+          poetry install
+      - name: test release
+        run: |
+          poetry config repositories.testpypi https://test.pypi.org/legacy/
+          poetry publish --build -r testpypi --username __token__ --password ${{ secrets.TEST_PYPI_TOKEN }}
+
   releasetestcheck:
     name: release test check
     needs: releasetest
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: [3.9]
+        python-version: [3.11]
 
     # Steps represent a sequence of tasks that will be executed as part of the job
     steps:
@@ -117,82 +117,82 @@ jobs:
       - name: Test
         run: |
           pytest tests/
-          
+
   release:
     name: release
     needs: [releasetestcheck, tagging]
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: [3.9]
+        python-version: [3.11]
 
     # Steps represent a sequence of tasks that will be executed as part of the job
     steps:
-    - name: Get the version
-      id: get_version
-      run: |
-        echo ::set-output name=TAG::`echo $SOURCE_VERSION | cut -d / -f 2`
-      env:
-        SOURCE_VERSION: ${{ github.event.pull_request.head.ref }}
-    - uses: actions/checkout@v2
-    - name: Set up Python ${{ matrix.python-version }}
-      uses: actions/setup-python@v2.2.2
-      with:
-        python-version: ${{ matrix.python-version }}
-    - name: Install dependencies
-      run: |
-        python -m pip install --upgrade pip setuptools wheel
-        python -m pip install poetry
-        poetry install
-    - name: release
-      run: |
-        poetry publish --build --username __token__ --password ${{ secrets.PYPI_TOKEN }}
-    - name: Create release
-      id: create_release
-      uses: actions/create-release@v1
-      env:
-        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
-      with:
-        tag_name: ${{ steps.get_version.outputs.TAG }}
-        release_name: ${{ steps.get_version.outputs.TAG }}
-        draft: false
-        prerelease: false
-        body: |
-          ${{ github.event.pull_request.body }}
-          
-          This release is automatically generated.
-          Please see the pull request.
-          [${{ github.event.pull_request.html_url }}](${{ github.event.pull_request.html_url }})
-    - name: Generate checksum
-      run: |
-        cd dist; sha256sum * > checksums.txt; cd -
-    - name: Upload tar.gz
-      uses: actions/upload-release-asset@v1
-      env:
-        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
-      with:
-        upload_url: ${{ steps.create_release.outputs.upload_url }}
-        asset_path: dist/pams-${{ steps.get_version.outputs.TAG }}.tar.gz
-        asset_name: pams-${{ steps.get_version.outputs.TAG }}.tar.gz
-        asset_content_type: application/gzip
-    - name: Upload whl
-      uses: actions/upload-release-asset@v1
-      env:
-        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
-      with:
-        upload_url: ${{ steps.create_release.outputs.upload_url }}
-        asset_path: dist/pams-${{ steps.get_version.outputs.TAG }}-py3-none-any.whl
-        asset_name: pams-${{ steps.get_version.outputs.TAG }}-py3-none-any.whl
-        asset_content_type: application/x-pywheel+zip
-    - name: Upload checksum
-      uses: actions/upload-release-asset@v1
-      env:
-        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
-      with:
-        upload_url: ${{ steps.create_release.outputs.upload_url }}
-        asset_path: dist/checksums.txt
-        asset_name: pams-${{ steps.get_version.outputs.TAG }}-checksums.txt
-        asset_content_type: text/plain
-    - name: remove branch
-      run: |
-        git push --delete origin ${{ github.event.pull_request.head.ref }}
+      - name: Get the version
+        id: get_version
+        run: |
+          echo ::set-output name=TAG::`echo $SOURCE_VERSION | cut -d / -f 2`
+        env:
+          SOURCE_VERSION: ${{ github.event.pull_request.head.ref }}
+      - uses: actions/checkout@v2
+      - name: Set up Python ${{ matrix.python-version }}
+        uses: actions/setup-python@v2.2.2
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Install dependencies
+        run: |
+          python -m pip install --upgrade pip setuptools wheel
+          python -m pip install poetry
+          poetry install
+      - name: release
+        run: |
+          poetry publish --build --username __token__ --password ${{ secrets.PYPI_TOKEN }}
+      - name: Create release
+        id: create_release
+        uses: actions/create-release@v1
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+        with:
+          tag_name: ${{ steps.get_version.outputs.TAG }}
+          release_name: ${{ steps.get_version.outputs.TAG }}
+          draft: false
+          prerelease: false
+          body: |
+            ${{ github.event.pull_request.body }}
+
+            This release is automatically generated.
+            Please see the pull request.
+            [${{ github.event.pull_request.html_url }}](${{ github.event.pull_request.html_url }})
+      - name: Generate checksum
+        run: |
+          cd dist; sha256sum * > checksums.txt; cd -
+      - name: Upload tar.gz
+        uses: actions/upload-release-asset@v1
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+        with:
+          upload_url: ${{ steps.create_release.outputs.upload_url }}
+          asset_path: dist/pams-${{ steps.get_version.outputs.TAG }}.tar.gz
+          asset_name: pams-${{ steps.get_version.outputs.TAG }}.tar.gz
+          asset_content_type: application/gzip
+      - name: Upload whl
+        uses: actions/upload-release-asset@v1
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+        with:
+          upload_url: ${{ steps.create_release.outputs.upload_url }}
+          asset_path: dist/pams-${{ steps.get_version.outputs.TAG }}-py3-none-any.whl
+          asset_name: pams-${{ steps.get_version.outputs.TAG }}-py3-none-any.whl
+          asset_content_type: application/x-pywheel+zip
+      - name: Upload checksum
+        uses: actions/upload-release-asset@v1
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+        with:
+          upload_url: ${{ steps.create_release.outputs.upload_url }}
+          asset_path: dist/checksums.txt
+          asset_name: pams-${{ steps.get_version.outputs.TAG }}-checksums.txt
+          asset_content_type: text/plain
+      - name: remove branch
+        run: |
+          git push --delete origin ${{ github.event.pull_request.head.ref }}
diff --git a/pams/logs/__init__.py b/pams/logs/__init__.py
index 2f4826b2..08c62832 100644
--- a/pams/logs/__init__.py
+++ b/pams/logs/__init__.py
@@ -1,5 +1,6 @@
 from .base import CancelLog
 from .base import ExecutionLog
+from .base import ExpirationLog
 from .base import Log
 from .base import Logger
 from .base import MarketStepBeginLog
diff --git a/pams/logs/base.py b/pams/logs/base.py
index 134dbbdd..6b722330 100644
--- a/pams/logs/base.py
+++ b/pams/logs/base.py
@@ -120,6 +120,51 @@ def __init__(
         # TODO: Type validation
 
 
+class ExpirationLog(Log):
+    """Expiration type log class.
+
+    This log is usually generated when an order is expired on markets.
+    """
+
+    def __init__(
+        self,
+        order_id: Optional[int],
+        market_id: int,
+        time: int,
+        order_time: Optional[int],
+        agent_id: int,
+        is_buy: bool,
+        kind: OrderKind,
+        volume: int,
+        price: Optional[float] = None,
+        ttl: Optional[int] = None,
+    ):
+        """initialize
+
+        Args:
+            order_id (int): order ID.
+            market_id (int): market ID.
+            time (int): time.
+            order_time (int): time to order.
+            agent_id (int): agent ID.
+            is_buy (bool): whether it is a buy order or not.
+            kind (:class:`pams.order.OrderKind`): kind of order.
+            volume (int): order volume.
+            price (float, Optional): order price.
+            ttl (int, Optional): time to order expiration.
+        """
+        self.order_id: Optional[int] = order_id
+        self.market_id: int = market_id
+        self.time: int = time
+        self.order_time: Optional[int] = order_time
+        self.agent_id: int = agent_id
+        self.is_buy: bool = is_buy
+        self.kind: OrderKind = kind
+        self.price: Optional[float] = price
+        self.volume: int = volume
+        self.ttl: Optional[int] = ttl
+
+
 class ExecutionLog(Log):
     """Execution type log class.
 
@@ -352,6 +397,8 @@ def process(self, logs: List["Log"]) -> None:
                 self.process_order_log(log=log)
             elif isinstance(log, CancelLog):
                 self.process_cancel_log(log=log)
+            elif isinstance(log, ExpirationLog):
+                self.process_expiration_log(log=log)
             elif isinstance(log, ExecutionLog):
                 self.process_execution_log(log=log)
             elif isinstance(log, SimulationBeginLog):
@@ -390,6 +437,17 @@ def process_cancel_log(self, log: "CancelLog") -> None:
         """
         pass
 
+    def process_expiration_log(self, log: "ExpirationLog") -> None:
+        """process expiration log. Called from :func:`process`.
+
+        Args:
+            log (:class:`pams.logs.ExpirationLog`]): expiration log
+
+        Returns:
+            None
+        """
+        pass
+
     def process_execution_log(self, log: "ExecutionLog") -> None:
         """process execution log. Called from :func:`process`.
 
diff --git a/pams/market.py b/pams/market.py
index 3b9d7936..57a7f509 100644
--- a/pams/market.py
+++ b/pams/market.py
@@ -14,6 +14,7 @@
 
 from .logs.base import CancelLog
 from .logs.base import ExecutionLog
+from .logs.base import ExpirationLog
 from .logs.base import Log
 from .logs.base import Logger
 from .logs.base import OrderLog
@@ -551,8 +552,14 @@ def _set_time(self, time: int, next_fundamental_price: float) -> None:
             None
         """
         self.time = time
-        self.buy_order_book._set_time(time)
-        self.sell_order_book._set_time(time)
+        logs: List[ExpirationLog] = self.buy_order_book._set_time(time)
+        if self.logger is not None:
+            for log in logs:
+                log.read_and_write(logger=self.logger)
+        logs_: List[ExpirationLog] = self.sell_order_book._set_time(time)
+        if self.logger is not None:
+            for log_ in logs_:
+                log_.read_and_write(logger=self.logger)
         self._fill_until(time=time)
         self._fundamental_prices[self.time] = next_fundamental_price
         if self.time > 0:
@@ -599,8 +606,14 @@ def _update_time(self, next_fundamental_price: float) -> None:
             None
         """
         self.time += 1
-        self.buy_order_book._set_time(self.time)
-        self.sell_order_book._set_time(self.time)
+        logs: List[ExpirationLog] = self.buy_order_book._set_time(self.time)
+        if self.logger is not None:
+            for log in logs:
+                log.read_and_write(logger=self.logger)
+        logs_: List[ExpirationLog] = self.sell_order_book._set_time(self.time)
+        if self.logger is not None:
+            for log_ in logs_:
+                log_.read_and_write(logger=self.logger)
         self._fill_until(time=self.time)
         self._fundamental_prices[self.time] = next_fundamental_price
         if self.time > 0:
diff --git a/pams/order_book.py b/pams/order_book.py
index 8f3413d5..341ab56e 100644
--- a/pams/order_book.py
+++ b/pams/order_book.py
@@ -3,6 +3,7 @@
 from typing import List
 from typing import Optional
 
+from .logs.base import ExpirationLog
 from .order import Cancel
 from .order import Order
 
@@ -122,8 +123,12 @@ def change_order_volume(self, order: Order, delta: int) -> None:
         if order.volume < 0:
             raise AssertionError
 
-    def _check_expired_orders(self) -> None:
-        """check and delete expired orders. (Internal Method)"""
+    def _check_expired_orders(self) -> List[ExpirationLog]:
+        """check and delete expired orders. (Internal Method)
+
+        Returns:
+            List[ExpirationLog]: the list of expiration logs.
+        """
         delete_orders: List[Order] = sum(
             [value for key, value in self.expire_time_list.items() if key < self.time],
             [],
@@ -131,26 +136,42 @@ def _check_expired_orders(self) -> None:
         delete_keys: List[int] = [
             key for key, value in self.expire_time_list.items() if key < self.time
         ]
+        logs: List[ExpirationLog] = []
         if len(delete_orders) == 0:
-            return
+            return logs
         # TODO: think better sorting in the following 3 lines
         for delete_order in delete_orders:
+            log: ExpirationLog = ExpirationLog(
+                order_id=delete_order.order_id,
+                market_id=delete_order.market_id,
+                time=self.time,
+                order_time=delete_order.placed_at,
+                agent_id=delete_order.agent_id,
+                is_buy=delete_order.is_buy,
+                kind=delete_order.kind,
+                volume=delete_order.volume,
+                price=delete_order.price,
+                ttl=delete_order.ttl,
+            )
+            logs.append(log)
             self.priority_queue.remove(delete_order)
         heapq.heapify(self.priority_queue)
         for key in delete_keys:
             self.expire_time_list.pop(key)
+        return logs
 
-    def _set_time(self, time: int) -> None:
+    def _set_time(self, time: int) -> List[ExpirationLog]:
         """set time step. (Usually, it is called from market.)
 
         Args:
             time (int): time step.
 
         Returns:
-            None
+            List[ExpirationLog]: the list of expiration logs.
         """
         self.time = time
-        self._check_expired_orders()
+        logs: List[ExpirationLog] = self._check_expired_orders()
+        return logs
 
     def _update_time(self) -> None:
         """update time. (Usually, it is called from market.)
diff --git a/pams/version.py b/pams/version.py
index d3ec452c..3ced3581 100644
--- a/pams/version.py
+++ b/pams/version.py
@@ -1 +1 @@
-__version__ = "0.2.0"
+__version__ = "0.2.1"
diff --git a/pyproject.toml b/pyproject.toml
index 88bfe329..6a172774 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [tool.poetry]
 name = "pams"
-version = "0.2.0"
+version = "0.2.1"
 description = "PAMS: Platform for Artificial Market Simulations"
 authors = ["Masanori HIRANO <masa.hirano.1996@gmail.com>", "Ryosuke TAKATA <ryos427@yahoo.co.jp>", "Kiyoshi IZUMI"]
 license = "epl-1.0"
diff --git a/tests/pams/logs/test_base.py b/tests/pams/logs/test_base.py
index dd3f0fd7..7410a8b9 100644
--- a/tests/pams/logs/test_base.py
+++ b/tests/pams/logs/test_base.py
@@ -10,6 +10,7 @@
 from pams import Simulator
 from pams.logs import CancelLog
 from pams.logs import ExecutionLog
+from pams.logs import ExpirationLog
 from pams.logs import Log
 from pams.logs import Logger
 from pams.logs import MarketStepBeginLog
@@ -140,6 +141,53 @@ def test__init__(self) -> None:
         assert log.ttl is None
 
 
+class TestExpirationLog:
+    def test__init__(self) -> None:
+        log = ExpirationLog(
+            order_id=2,
+            market_id=3,
+            time=10,
+            order_time=8,
+            agent_id=4,
+            is_buy=True,
+            kind=LIMIT_ORDER,
+            volume=10,
+            price=100.0,
+            ttl=2,
+        )
+        assert log.order_id == 2
+        assert log.market_id == 3
+        assert log.time == 10
+        assert log.order_time == 8
+        assert log.agent_id == 4
+        assert log.is_buy is True
+        assert log.kind == LIMIT_ORDER
+        assert log.volume == 10
+        assert log.price == 100.0
+        assert log.ttl == 2
+
+        log = ExpirationLog(
+            order_id=2,
+            market_id=3,
+            time=10,
+            order_time=8,
+            agent_id=4,
+            is_buy=True,
+            kind=MARKET_ORDER,
+            volume=10,
+        )
+        assert log.order_id == 2
+        assert log.market_id == 3
+        assert log.time == 10
+        assert log.order_time == 8
+        assert log.agent_id == 4
+        assert log.is_buy is True
+        assert log.kind == MARKET_ORDER
+        assert log.volume == 10
+        assert log.price is None
+        assert log.ttl is None
+
+
 class TestExecutionLog:
     def test___init__(self) -> None:
         log = ExecutionLog(
@@ -329,6 +377,7 @@ def __init__(self) -> None:
                 super().__init__()
                 self.n_order_log = 0
                 self.n_cancel_log = 0
+                self.n_expiration_log = 0
                 self.n_execution_log = 0
                 self.n_simulation_begin_log = 0
                 self.n_simulation_end_log = 0
@@ -343,6 +392,9 @@ def process_order_log(self, log: OrderLog) -> None:
             def process_cancel_log(self, log: CancelLog) -> None:
                 self.n_cancel_log += 1
 
+            def process_expiration_log(self, log: ExpirationLog) -> None:
+                self.n_expiration_log += 1
+
             def process_execution_log(self, log: ExecutionLog) -> None:
                 self.n_execution_log += 1
 
@@ -400,6 +452,19 @@ def process_market_step_end_log(self, log: MarketStepEndLog) -> None:
             ttl=9,
         )
         logger.write(log=cancel_log)
+        expiration_log = ExpirationLog(
+            order_id=1,
+            market_id=2,
+            time=5,
+            order_time=3,
+            agent_id=4,
+            is_buy=True,
+            kind=LIMIT_ORDER,
+            volume=6,
+            price=7.0,
+            ttl=2,
+        )
+        logger.write(log=expiration_log)
         execution_log = ExecutionLog(
             market_id=1,
             time=2,
@@ -435,6 +500,7 @@ def process_market_step_end_log(self, log: MarketStepEndLog) -> None:
 
         assert logger.n_order_log == 1
         assert logger.n_cancel_log == 1
+        assert logger.n_expiration_log == 1
         assert logger.n_execution_log == 1
         assert logger.n_simulation_begin_log == 1
         assert logger.n_simulation_end_log == 1
@@ -481,6 +547,19 @@ def test_process2(self) -> None:
             ttl=9,
         )
         logger.write(log=cancel_log)
+        expiration_log = ExpirationLog(
+            order_id=1,
+            market_id=2,
+            time=5,
+            order_time=3,
+            agent_id=4,
+            is_buy=True,
+            kind=LIMIT_ORDER,
+            volume=6,
+            price=7.0,
+            ttl=2,
+        )
+        logger.write(log=expiration_log)
         execution_log = ExecutionLog(
             market_id=1,
             time=2,
diff --git a/tests/pams/test_market.py b/tests/pams/test_market.py
index 83e35ba3..839d4b59 100644
--- a/tests/pams/test_market.py
+++ b/tests/pams/test_market.py
@@ -13,6 +13,7 @@
 from pams import Cancel
 from pams import Market
 from pams import Order
+from pams.logs.base import ExpirationLog
 from pams.logs.base import Logger
 from pams.simulator import Simulator
 
@@ -749,3 +750,54 @@ def test_execution_order_pattern10(self) -> None:
         assert market.remain_executable_orders()
         logs = market._execution()
         assert len(logs) == 2
+
+    def test_expiration_orrder_pattern01(self) -> None:
+        logger = Logger()
+        market = self.base_class(
+            market_id=0,
+            prng=random.Random(42),
+            logger=logger,
+            simulator=Simulator(prng=random.Random(42)),
+            name="test",
+        )
+        market._update_time(1.0)
+        market._is_running = True
+        order = Order(
+            agent_id=0, market_id=0, is_buy=False, kind=MARKET_ORDER, volume=2, ttl=1
+        )
+        market._add_order(order)
+        order = Order(
+            agent_id=0, market_id=0, is_buy=True, kind=MARKET_ORDER, volume=1, ttl=1
+        )
+        market._add_order(order)
+        market._update_time(1.0)
+        market._update_time(1.0)
+        assert (
+            len([log for log in logger.pending_logs if isinstance(log, ExpirationLog)])
+            == 2
+        )
+
+    def test_expiration_orrder_pattern02(self) -> None:
+        logger = Logger()
+        market = self.base_class(
+            market_id=0,
+            prng=random.Random(42),
+            logger=logger,
+            simulator=Simulator(prng=random.Random(42)),
+            name="test",
+        )
+        market._update_time(1.0)
+        market._is_running = True
+        order = Order(
+            agent_id=0, market_id=0, is_buy=False, kind=MARKET_ORDER, volume=2, ttl=1
+        )
+        market._add_order(order)
+        order = Order(
+            agent_id=0, market_id=0, is_buy=True, kind=MARKET_ORDER, volume=1, ttl=1
+        )
+        market._add_order(order)
+        market._set_time(time=2, next_fundamental_price=1.0)
+        assert (
+            len([log for log in logger.pending_logs if isinstance(log, ExpirationLog)])
+            == 2
+        )