diff --git a/CHANGELOG.md b/CHANGELOG.md
index 1ce50eda..0bab3faf 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,6 +6,7 @@
 
 #### Fixes
 
+* [#905](https://github.com/ruby-grape/grape-swagger/pull/905): Allow Float, BigDecimal and beginless ranges in `values` to set `minimum` and `maximum`, and skip infinite bounds that cannot be serialized to JSON - [@artyomb](https://github.com/artyomb).
 * [#1016](https://github.com/ruby-grape/grape-swagger/pull/1016): Hide the nested parameters of a Hash parameter marked `documentation: { hidden: true }`, and pass the resolved `token_owner` to parameter-level `hidden:` procs like route-level ones (raising `TokenOwnerNotFound` if the configured method is missing) - [@numbata](https://github.com/numbata).
 * [#1013](https://github.com/ruby-grape/grape-swagger/pull/1013): Fix array `default` values being placed inside `items` instead of on the array parameter or property, and emit an empty array `default` - [@numbata](https://github.com/numbata).
 * [#1012](https://github.com/ruby-grape/grape-swagger/pull/1012): Keep the Danger PR check running in CI by pinning `git` below 6 - [@numbata](https://github.com/numbata).
diff --git a/lib/grape-swagger/doc_methods/move_params.rb b/lib/grape-swagger/doc_methods/move_params.rb
index fd1823e1..e92d647e 100644
--- a/lib/grape-swagger/doc_methods/move_params.rb
+++ b/lib/grape-swagger/doc_methods/move_params.rb
@@ -178,8 +178,8 @@ def parse_model(ref)
         end
 
         def property_keys
-          %i[type format description minimum maximum items enum default additional_properties additionalProperties
-             example minLength maxLength minProperties maxProperties]
+          %i[type format description minimum maximum exclusiveMaximum items enum default additional_properties
+             additionalProperties example minLength maxLength minProperties maxProperties]
         end
 
         def array_schema_keys
diff --git a/lib/grape-swagger/doc_methods/parse_params.rb b/lib/grape-swagger/doc_methods/parse_params.rb
index 3e12889d..4350a482 100644
--- a/lib/grape-swagger/doc_methods/parse_params.rb
+++ b/lib/grape-swagger/doc_methods/parse_params.rb
@@ -193,7 +193,7 @@ def parse_enum_or_range_values(values)
           when Proc
             parse_enum_or_range_values(values.call) if values.parameters.empty?
           when Range
-            parse_range_values(values) if values.first.is_a?(Integer)
+            parse_range_values(values) if range_bounds_real?(values)
           when Array
             { enum: values }
           else
@@ -202,7 +202,26 @@ def parse_enum_or_range_values(values)
         end
 
         def parse_range_values(values)
-          { minimum: values.begin, maximum: values.end }.compact
+          range = { minimum: range_bound(values.begin), maximum: range_bound(values.end) }.compact
+          range[:exclusiveMaximum] = true if values.exclude_end? && range.key?(:maximum)
+          range
+        end
+
+        def range_bounds_real?(values)
+          bounds = [values.begin, values.end].compact
+          bounds.any? && bounds.all? { |bound| real_number?(bound) }
+        end
+
+        def real_number?(bound)
+          bound.is_a?(Numeric) && bound.real?
+        end
+
+        # Only finite numbers are valid JSON; BigDecimal and Rational are emitted as Integer when whole, else Float.
+        def range_bound(bound)
+          return unless real_number?(bound) && bound.finite?
+          return bound if bound.is_a?(Integer) || bound.is_a?(Float)
+
+          bound.to_i == bound ? bound.to_i : bound.to_f
         end
       end
     end
diff --git a/spec/lib/parse_params_spec.rb b/spec/lib/parse_params_spec.rb
index 51e82f71..4a4ac205 100644
--- a/spec/lib/parse_params_spec.rb
+++ b/spec/lib/parse_params_spec.rb
@@ -37,6 +37,94 @@
         end
       end
 
+      describe 'first Float' do
+        specify do
+          parsed_range = subject.send(:parse_enum_or_range_values, -5.0..5.0)
+          expect(parsed_range).to eql(minimum: -5.0, maximum: 5.0)
+        end
+      end
+
+      describe 'with an infinite end' do
+        specify do
+          expect(subject.send(:parse_enum_or_range_values, 1.0..Float::INFINITY)).to eql(minimum: 1.0)
+          expect(subject.send(:parse_enum_or_range_values, 1..Float::INFINITY)).to eql(minimum: 1)
+        end
+      end
+
+      describe 'with an infinite begin' do
+        specify do
+          parsed_range = subject.send(:parse_enum_or_range_values, -Float::INFINITY..5.0)
+          expect(parsed_range).to eql(maximum: 5.0)
+        end
+      end
+
+      describe 'beginless' do
+        specify do
+          expect(subject.send(:parse_enum_or_range_values, ..5.0)).to eql(maximum: 5.0)
+          expect(subject.send(:parse_enum_or_range_values, ..5)).to eql(maximum: 5)
+        end
+      end
+
+      describe 'endless Float' do
+        specify do
+          parsed_range = subject.send(:parse_enum_or_range_values, 1.5..)
+          expect(parsed_range).to eql(minimum: 1.5)
+        end
+      end
+
+      describe 'BigDecimal' do
+        specify do
+          parsed_range = subject.send(:parse_enum_or_range_values, BigDecimal('1')..BigDecimal('2.5'))
+          expect(parsed_range).to eql(minimum: 1, maximum: 2.5)
+        end
+
+        it 'keeps whole values beyond Float precision exact' do
+          parsed_range = subject.send(:parse_enum_or_range_values, BigDecimal('9007199254740993')..)
+          expect(parsed_range).to eql(minimum: 9_007_199_254_740_993)
+        end
+
+        it 'skips NaN and infinite bounds' do
+          expect(subject.send(:parse_enum_or_range_values, ..BigDecimal('NaN'))).to eql({})
+          expect(subject.send(:parse_enum_or_range_values, BigDecimal('-Infinity')..BigDecimal('3'))).to eql(maximum: 3)
+        end
+      end
+
+      describe 'Rational' do
+        specify do
+          parsed_range = subject.send(:parse_enum_or_range_values, 1r..3/2r)
+          expect(parsed_range).to eql(minimum: 1, maximum: 1.5)
+        end
+      end
+
+      describe 'Float NaN' do
+        specify do
+          parsed_range = subject.send(:parse_enum_or_range_values, Float::NAN..)
+          expect(parsed_range).to eql({})
+        end
+      end
+
+      describe 'with an exclusive end' do
+        specify do
+          expect(subject.send(:parse_enum_or_range_values, 1...5))
+            .to eql(minimum: 1, maximum: 5, exclusiveMaximum: true)
+          expect(subject.send(:parse_enum_or_range_values, 0.0...1.0))
+            .to eql(minimum: 0.0, maximum: 1.0, exclusiveMaximum: true)
+        end
+
+        it 'does not flag an endless or infinite end' do
+          expect(subject.send(:parse_enum_or_range_values, 1...)).to eql(minimum: 1)
+          expect(subject.send(:parse_enum_or_range_values, 1.0...Float::INFINITY)).to eql(minimum: 1.0)
+        end
+      end
+
+      describe 'with Complex bounds' do
+        specify do
+          expect(subject.send(:parse_enum_or_range_values, ..Complex(1, 2))).to be_nil
+          expect(subject.send(:parse_enum_or_range_values, Complex(1, 2)..)).to be_nil
+          expect(subject.send(:parse_enum_or_range_values, 1..Complex(2, 0))).to be_nil
+        end
+      end
+
       describe 'first String' do
         specify do
           parsed_range = subject.send(:parse_enum_or_range_values, 'a'..'z')
diff --git a/spec/swagger_v2/param_values_spec.rb b/spec/swagger_v2/param_values_spec.rb
index 0220a9e7..b4a7b109 100644
--- a/spec/swagger_v2/param_values_spec.rb
+++ b/spec/swagger_v2/param_values_spec.rb
@@ -139,6 +139,47 @@ def app
         { message: 'hi' }
       end
 
+      desc 'range_infinite_float' do
+        consumes ['application/x-www-form-urlencoded']
+      end
+      params do
+        requires :float, type: Float, values: 1.0..Float::INFINITY
+      end
+      post :range_infinite_float do
+        { message: 'hi' }
+      end
+
+      desc 'range_exclusive_float' do
+        consumes ['application/x-www-form-urlencoded']
+      end
+      params do
+        requires :float, type: Float, values: 0.0...1.0
+      end
+      post :range_exclusive_float do
+        { message: 'hi' }
+      end
+
+      desc 'range_exclusive_body' do
+        consumes ['application/json']
+      end
+      params do
+        requires :float, type: Float, values: 0.0...1.0
+        requires :list, type: Array[Integer], values: 1...5
+      end
+      post :range_exclusive_body do
+        { message: 'hi' }
+      end
+
+      desc 'range_exclusive_query_array' do
+        consumes ['application/json']
+      end
+      params do
+        requires :list, type: Array[Integer], values: 1...5
+      end
+      get :range_exclusive_query_array do
+        { message: 'hi' }
+      end
+
       add_swagger_documentation
     end
   end
@@ -167,13 +208,55 @@ def first_parameter_info(request)
   context 'Range values' do
     subject(:range_float) { first_parameter_info('range_float') }
 
-    it 'has float range values as string' do
+    it 'has float range values as minimum and maximum' do
       expect(range_float).to eq [{
         'in' => 'formData',
         'name' => 'float',
         'type' => 'number',
         'required' => true,
-        'format' => 'float'
+        'format' => 'float',
+        'minimum' => -5.0,
+        'maximum' => 5.0
+      }]
+    end
+  end
+
+  context 'Range values with an exclusive end' do
+    subject(:range_exclusive_float) { first_parameter_info('range_exclusive_float') }
+
+    it 'flags the maximum as exclusive' do
+      expect(range_exclusive_float.first).to include('minimum' => 0.0, 'maximum' => 1.0, 'exclusiveMaximum' => true)
+    end
+  end
+
+  context 'Range values with an exclusive end in a query array' do
+    it 'keeps exclusiveMaximum on the array items' do
+      get '/swagger_doc/range_exclusive_query_array'
+      parameters = JSON.parse(last_response.body)['paths']['/range_exclusive_query_array']['get']['parameters']
+      expect(parameters.first['items']).to include('minimum' => 1, 'maximum' => 5, 'exclusiveMaximum' => true)
+    end
+  end
+
+  context 'Range values with an exclusive end in a body definition' do
+    it 'keeps exclusiveMaximum on properties and array items' do
+      get '/swagger_doc/range_exclusive_body'
+      props = JSON.parse(last_response.body)['definitions']['postRangeExclusiveBody']['properties']
+      expect(props['float']).to include('maximum' => 1.0, 'exclusiveMaximum' => true)
+      expect(props['list']['items']).to include('minimum' => 1, 'maximum' => 5, 'exclusiveMaximum' => true)
+    end
+  end
+
+  context 'Range values with an infinite end' do
+    subject(:range_infinite_float) { first_parameter_info('range_infinite_float') }
+
+    it 'has only the finite bound as minimum' do
+      expect(range_infinite_float).to eq [{
+        'in' => 'formData',
+        'name' => 'float',
+        'type' => 'number',
+        'required' => true,
+        'format' => 'float',
+        'minimum' => 1.0
       }]
     end
   end