On a recent chilly afternoon, Caruso cut a rakish figure strolling through the hotel’s Manor House in a snug gray double-breasted suit, wearing dark glasses and trailing behind his leashed dog Dodge — very much carrying himself like the man Forbes said is worth $4 billion. The docile golden retriever is his constant companion and later fell asleep at Caruso’s feet as he sat in the Miramar’s main restaurant, Malibu Farm, which serves farm-to-table fare.