[monte_carlo] two issues

[DaichiSudou]

There are two issues in this chapter.

1. The "more realistic dynamics" has infinite mean.
   In the simplest case where rho=0, S_1 is the exponential of the exponential of a Gaussian random variable (with some scalar), which is known to have infinite mean (it is indifinite integral of exp(exp(x)-x^2/2) with some scalar). Therefore, all the arguments that rely on finite mean become invalid.
2. There is an opportunity of arbitrage for the underlying asset, whose stochastic process S_n of prices is exogenously given.
   For example, in the "simple dynamics"(which has finite mean), you have an opportunity to arbitrage, unless the parameters happen to satisfy beta * exp(mu + sigma^2/2) =1.
   If beta * exp(mu + sigma^2/2) > 1, in t = 0, you buy the underlying asset at price S_0 and sell a forward contract at price beta * S_0 * exp(mu + sigma^2/2). You can get positive expented benefit at t=0.
   The default parameter values in the code are chosen so that the above equality is not satisfied, which contradicts "we determine the price of a given asset according to its expected payoff".