Referring to the 1973 Black-Scholes paper, the main assumption is that “The stock price follows a random walk in continuous time with a variance rate proportional to the square of the stock price. Thus the distribution of possible stock prices at the end of any finite interval is lognormal. The var...

I've had some numerical classes generated by AI with bad numerics. I recently asked a question for research and it just gave me some code which I then decided to use but the AI had used the Big Ball of Mud anti-pattern so I manually separated out 3 or 4 classes. I've since wondered whether I could h...

Keep using the old compiler, if it works for them! But hobbling the modern C++ with old stuff just helps to make C++ obsolete. If you were starting a new software project from scratch, what would make you choose C++? My choice of language almost certainly depends on the libraries available. e.g. A ...

No, averaged trajectories serve to validate the model against the standard SIR model. The stochastic model on a complete graph is useless, the average when applied to a social network and its confidence intervals is useful.

The game, when scaled, averages to the standard SIR model. If I remember correctly the computer played it with R0 = 2, 3 and 4. The ratio of growth to exponential growth is logit-normally distributed. Note that the model debunks huge numbers of stochastic SIR models in which the modellers just make ...

ASSetStudent: The cross-section of expected stock returns. I think that I might have solved that one. Offset returns => Normal distribution => Brownian motion Linear returns => Log-normal distribution => Geometric Brownian motion Affine returns => Mixture distribution => Geometric Brownian plus oth...

For symbolic algebra I've started using wxMaxima as it will simplify my expressions. SymPy would just return zero whereas MathCad would spin the fans until I killed the process.

The first question that I asked Grok was to explain how epidemics grow exponentially so it told me rather than correct me.

Alan. The Frequentist Guy might be confident (interval) but the Bayesian Gal would hardly find him credible (interval).

Paul I think your epidemic model looks dodgy. For a properly dodgy epidemic model you should play tag. Admittedly that looks a bit tiring so you could try playing cards with the same rules instead.

My model, which I call the minimal SIR model, is a discrete stochastic process that is also a card game. https://stochanswers.com/education/epidemic.html Do you know how an epidemic grows? One infects two, two infect four or three or two or one or none. All with different probabilities and a weighte...

My maths background is as a modeller. So is mine. Due to Covid I developed a minimal epidemic model which, of course, doesn't grow exponentially. i.e. Doesn't break the laws of Maths. And obviously I've complained about the accuracy of these models as well. I found those complaints informative and ...

Offset returns => Normal distribution => Brownian motion Linear returns => Log-Normal distribution => Geometric Brownian motion Affine returns => Log-Normal distribution + other => Geometric Brownian motion + other Where other appears to be a logit-normal distribution stretched out. Over time you g...