For people that get triggered when seeing math equations -- just read the key to see what goes into the equation to understand it. The greek stuff and symbols just tell us the math operation that's taking place (e.g sum all, transpose, multiply the series, etc.) so that anyone can replicate it.
I meant your definition of risk, not some book definition. Try to keep it above newbie level this time. Risk and probability are not one and the same. And yes also I am familiar with Calculus symbols and many of their operations.
I gave you my personal definition. Risk to me is 1) total capital loss or 2) not hitting a goal (estimation error in probability). What is risk to you?
An event happening or not happening. Not my personal definition, it just is. Also, even if you didn't ask, risk is not losing X number or percent of dollars - as so many think.
risk is precisely losing X percent or dollars. If you can’t lose X percent or dollars then you have no risk. You can make up your own alternative definitions of things but this is the commonly accepted definition in finance. (As an aside arbitrage is risk less profit because you can earn without any chance of financial losses) Where risk varies is in how one determines X percent or dollars. There are two schools of thought: Graham and Dodd and markowitz. Markowitz looks at the path dependency so it will take into account sharpe ratios and volatility. Graham and Dodd can also be worded as Permanent Impairment of a capital. most hedge funds and active traders view their risks In a markowitz framework. Warren Buffet and other deep fundamental guys view their risk in a Graham and Dodd. your stop losses are your risk. It’s how much you can lose.
probability and exposure are not the same. You can have exposure (pnl impact) to a very unlikely event or to a very likely event. Obviously you would view the two very differently.