entropy_pooling function

Numerical Entropy Minimization

This function solves the entropy minimization problem with equality and inequality constraints. The solution is a vector of posterior probabilities that distorts the least the prior (equal-weights probabilities) given the constraints (views on the market).

entropy_pooling(
  p,
  A = NULL,
  b = NULL,
  Aeq = NULL,
  beq = NULL,
  solver = c("nlminb", "solnl", "nloptr"),
  ...
)

Arguments

• p: A vector of prior probabilities.
• A: The linear inequality constraint (left-hand side).
• b: The linear inequality constraint (right-hand side).
• Aeq: The linear equality constraint (left-hand side).
• beq: The linear equality constraint (right-hand side).
• solver: A character. One of: "nlminb", "solnl" or "nloptr".
• ...: Further arguments passed to one of the solvers.

Returns

A vector of posterior probabilities.

Details

When imposing views constraints there is no need to specify the non-negativity constraint for probabilities, which is done automatically by entropy_pooling.

For the arguments accepted in ..., please see the documentation of nlminb, solnl, nloptr

and the examples bellow.

Examples

# setup
ret <- diff(log(EuStockMarkets))
n   <- nrow(ret)

# View on expected returns (here is 2% for each asset)
mean <- rep(0.02, 4)

# Prior probabilities (usually equal weight scheme)
prior <- rep(1 / n, n)

# View
views <- view_on_mean(x = ret, mean = mean)

# Optimization
ep <- entropy_pooling(
 p      = prior,
 Aeq    = views$Aeq,
 beq    = views$beq,
 solver = "nlminb"
)
ep

### Using the ... argument to control the optimization parameters

# nlminb
ep <- entropy_pooling(
 p      = prior,
 Aeq    = views$Aeq,
 beq    = views$beq,
 solver = "nlminb",
 control = list(
     eval.max = 1000,
     iter.max = 1000,
     trace    = TRUE
   )
)
ep

# nloptr
ep <- entropy_pooling(
 p      = prior,
 Aeq    = views$Aeq,
 beq    = views$beq,
 solver = "nloptr",
 control = list(
     xtol_rel = 1e-10,
     maxeval  = 1000,
     check_derivatives = TRUE
   )
)
ep