Here's a theory. Like Hannibal Lecter in Silence of the Lamb's, they simply found a dead man with Epstein's face. He, instead, is on his way to parts unknown. When you have zillions, anything is possible, including bribing the coroner. 

I will make a guess. If the payoffs are level invariant as in your examples, and you have 'continuous monitoring', and no cost-of-carry parameters, then what you want might follow simply from dimensional analysis of the value function. After all, you need dimensionless factors. But once you introduc...

If the derivative value is just the expectation of an arbitrary terminal payoff, then 'yes'. That follows from writing the value as an integral over a normal density with variance [$]\sigma^2 T[$] (times the payoff, of course). In other words, it's exactly the same normal density you would use to va...

With the exception of horizontal lines and maybe parabolas, I believe everything else requires numerics. 

I think GBM can hit every point on that circle! -- well, possibly excepting one, which doesn't matter. DavidJN's cite may be spot-on, although I haven't looked at that paper in years.  Off-hand, the horizontal line through A identifies two key times (t1,t2), and the GBM's location at t1 splits the p...

I am enjoying Hossenfelder's book. It's a good read for the beach, but maybe not that interesting to non-physicists (or non-ex-physicists). I'm about half-way through and she's bemoaning her seemingly endless search for the next temporary research position. So, it's a nice mix of general critique, i...

To me, a circle requires two dimensions. What are the two dimensions? 

You're welcome

Thanks.

No, first, I said "n is large but not infinite", so the puzzle is to provide an asymptotic formula that depends upon n. Keep thinking!

Second, if n were infinite, the expected max is [$]+\infty[$].

Hint: start from bearish's comment, generalize it, and start calculating. 

The late Graeme West, Wilmott mag, Fig. 2 quoting an alogorithm of Hart (accurate to machine double precision everywhere). 

Please justify the need for extreme speed. What is the application?

Or, the cookbook recipe to working with stochastic differential equations is the following multiplication table: [$]dt \times dt = dt \times dW_t = dW_t \times dt = 0 [$] [$]dW_t \times dW_t = dt[$] (All higher powers are zero). After all, to drive a car, you don't have to be a mechanic.   Of course...

If you set up the option value pde problem using x = log S with solution [$]f(x,t)[$], you can differentiate it to get the pde for [$]g(x,t) = f_x[$]. Then perhaps simply solve that second pde for [$]g[$] on a trinomial lattice, and convert to delta. You probably need two passes, the first to get t...

If you set up the option value pde problem using x = log S with solution [$]f(x,t)[$], you can differentiate it to get the pde for [$]g(x,t) = f_x[$]. Then perhaps simply solve that second pde for [$]g[$] on a trinomial lattice, and convert to delta. You probably need two passes, the first to get th...

It's usually solved backwards because of the "principle of optimality", which you can google if you don't know it. The standard finance example is determining an optimal exercise strategy for an American-style put. It's day 1 and the put expires on day N. Whatever the "strategy" on day 1, it should ...