Merge pull request #1 from stefansedlmair/stoch-aad-with-expectation

Stochastic AAD with Expectation Operator

Author: finmath.net

src/main/java/net/finmath/montecarlo/automaticdifferentiation/backward/RandomVariableDifferentiableAAD.java

@@ -100,6 +100,9 @@ private void propagateDerivativesFromResultToArgument(Map<Long, RandomVariableIn
 					RandomVariableInterface derivative			= derivatives.get(id);
 					RandomVariableInterface argumentDerivative	= derivatives.get(argumentID);
 
+					// Implementation of AVERAGE (see paper for details).
+					if(operator == OperatorType.AVERAGE) derivative = derivative.average();
+
 					argumentDerivative = argumentDerivative.addProduct(partialDerivative, derivative);
 
 					derivatives.put(argumentID, argumentDerivative);
@@ -139,7 +142,7 @@ private RandomVariableInterface getPartialDerivative(OperatorTreeNode differenti
 				resultrandomvariable = X.sin().mult(-1.0);
 				break;
 			case AVERAGE:
-				resultrandomvariable = new RandomVariable(X.size()).invert();
+				resultrandomvariable = new RandomVariable(1.0);
 				break;
 			case VARIANCE:
 				resultrandomvariable = X.sub(X.getAverage()*(2.0*X.size()-1.0)/X.size()).mult(2.0/X.size());

src/test/java/net/finmath/montecarlo/automaticdifferentiation/backward/RandomVariableDifferentiableInterfaceTest.java

@@ -14,13 +14,15 @@
 import org.junit.runners.Parameterized;
 import org.junit.runners.Parameterized.Parameters;
 
-import net.finmath.montecarlo.AbstractRandomVariableFactory;
+import net.finmath.montecarlo.BrownianMotion;
+import net.finmath.montecarlo.BrownianMotionInterface;
 import net.finmath.montecarlo.RandomVariable;
 import net.finmath.montecarlo.RandomVariableFactory;
 import net.finmath.montecarlo.automaticdifferentiation.AbstractRandomVariableDifferentiableFactory;
 import net.finmath.montecarlo.automaticdifferentiation.RandomVariableDifferentiableInterface;
 import net.finmath.montecarlo.automaticdifferentiation.backward.alternative.RandomVariableAADv2Factory;
 import net.finmath.stochastic.RandomVariableInterface;
+import net.finmath.time.TimeDiscretization;
 
 /**
  * Unit test for random variables implementing <code>RandomVariableDifferentiableInterface</code>.
@@ -346,6 +348,33 @@ public void testRandomVariableGradientBigSum2(){
 
 	}
 
+	@Test
+	public void testRandomVariableExpectation(){
+
+		int numberOfPaths = 100000;
+		int seed = 3141;
+		BrownianMotionInterface brownianMotion = new BrownianMotion(new TimeDiscretization(0.0, 1.0), 1 /* numberOfFactors */, numberOfPaths, seed);
+		RandomVariableInterface brownianIncrement = brownianMotion.getIncrement(0, 0);
+		
+		RandomVariableDifferentiableInterface x = randomVariableFactory.createRandomVariable(1.0);
+		
+		RandomVariableInterface y = x.mult(brownianIncrement.sub(brownianIncrement.average())).average().mult(brownianIncrement);
+
+		Map<Long, RandomVariableInterface> aadGradient = ((RandomVariableDifferentiableInterface) y).getGradient();
+
+		RandomVariableInterface derivative = aadGradient.get(x.getID());
+		
+		System.out.println(randomVariableFactory.toString());
+		System.out.println(y.getAverage());
+		System.out.println(brownianIncrement.squared().getAverage());
+		System.out.println((aadGradient.get(x.getID())).getAverage());
+
+		Assert.assertEquals(0.0, y.getAverage(), 1E-8);
+
+		// Test RandomVariableDifferentiableAADFactory (the others currently fail)
+		if(randomVariableFactory instanceof RandomVariableDifferentiableAADFactory) Assert.assertEquals(0.0, derivative.getAverage(), 1E-8);
+	}
+
 	@Test
 	public void testRandomVariableGradientBigSumWithConstants(){