Classic option pricing theory values a derivative contract via dynamic replication, and views the derivative as redundant relative to the replicating portfolio. In practice, while dynamic replication proves highly effective in drastically reducing the risk in derivative investments, the...

We generalize the Kelly criterion and the growth-optimal portfolio (GOP) concept beyond log-wealth maximization. We show that models of speculative price dynamics with time change require different compounding algebras leading to GOPs that do not coincide with log-wealth maximization. In...